existence of solutions for variational inequalities on riemannian manifolds abstract we establish the existence and uniqueness results for variational inequality problems on riemannian manifolds and solve completely the open problem proposed in s z nemeth variational inequalities on hadamard manifolds nonlinear anal 52 2003 1491 1498 also the relationships between the constrained optimization problem and the variational inequality problems as well as the projections on riemannian manifolds are studied

an iterative algorithm for solving fixed point problems variational inequality problems and mixed equilibrium problems abstract in this paper we introduce an iterative algorithm for finding a common element of the set of solutions of a mixed equilibrium problem the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of some variational inequality furthermore we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets our results extend and improve the corresponding results of zeng and yao l c zeng and j c yao a hybrid iterative scheme for mixed equilibrium problems and fixed point problems j comput appl math 214 2008 186 201 takahashi and takahashi s takahashi and w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 and many others

two extragradient methods for generalized mixed equilibrium problems nonexpansive mappings and monotone mappings in this paper we introduce iterative schemes based on the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of an infinite a finite family of nonexpansive mappings and the set of solutions of a variational inequality problem for a monotone lipschitz continuous mapping we obtain some weak convergence theorems for the sequences generated by these processes in hilbert spaces the results in this paper generalize extend and unify some well known weak convergence theorems in the literature

entropy like proximal methods in convex programming we study an extension of the proximal method for convex programming where the quadratic regularization kernel is substituted by a class of convex statistical distances called divergences which are typically entropy like in form after establishing several basic properties of these quasi distances we present a convergence analysis of the resulting entropy like proximal algorithm applying this algorithm to the dual of a convex program we recover a wide class of nonquadratic multiplier methods and prove their convergence

products of finitely many resolvents of maximal monotone mappings in reflexive banach spaces we propose two algorithms for finding common zeros of finitely many maximal monotone mappings in reflexive banach spaces these algorithms are based on the bregman distance related to a well chosen convex function and improve previous results finally we mention two applications of our algorithms for solving equilibrium problems and convex feasibility problems

decision making generalized by a cumulative probability weighting function abstract typical examples of intertemporal decision making involve situations in which individuals must choose between a smaller reward but more immediate and a larger one delivered later analogously probabilistic decision making involves choices between options whose consequences differ in relation to their probability of receiving in economics the expected utility theory eut and the discounted utility theory dut are traditionally accepted normative models for describing respectively probabilistic and intertemporal decision making a large number of experiments confirmed that the linearity assumed by the eut does not explain some observed behaviors as nonlinear preference risk seeking and loss aversion that observation led to the development of new theoretical models called non expected utility theories neut which include a nonlinear transformation of the probability scale an essential feature of the so called preference function of these theories is that the probabilities are transformed by decision weights by means of a cumulative probability weighting function w p we obtain in this article a generalized function for the probabilistic discount process this function has as particular cases mathematical forms already consecrated in the literature including discount models that consider effects of psychophysical perception we also propose a new generalized function for the functional form of w the limiting cases of this function encompass some parametric forms already proposed in the literature far beyond a mere generalization our function allows the interpretation of probabilistic decision making theories based on the assumption that individuals behave similarly in the face of probabilities and delays and is supported by phenomenological models

psychophysics of time perception and intertemporal choice models intertemporal choice and psychophysics of time perception have been attracting attention in econophysics and neuroeconomics several models have been proposed for intertemporal choice exponential discounting general hyperbolic discounting exponential discounting with logarithmic time perception of the weber fechner law a q exponential discount model based on tsallis s statistics simple hyperbolic discounting and stevens power law exponential discounting exponential discounting with stevens power time perception in order to examine the fitness of the models for behavioral data we estimated the parameters and aicc akaike information criterion with small sample correction of the intertemporal choice models by assessing the points of subjective equality indifference points at seven delays our results have shown that the orders of the goodness of fit for both group and individual data were weber fechner discounting general hyperbola stevens power law discounting simple hyperbolic discounting exponential discounting indicating that human time perception in intertemporal choice may follow the weber fechner law indications of the results for neuropsychopharmacological treatments of addiction and biophysical processing underlying temporal discounting and time perception are discussed

solutions of system of equilibrium and variational inequality problems on fixed points of infinite family of nonexpansive mappings in this paper we introduce a hybrid viscosity approximation scheme for finding a common element of the solution set for a system of equilibrium problems the solution set for a system of variational inequality problems and the common fixed point set for an infinite family of nonexpansive mappings in hilbert spaces then we prove the strong convergence of the proposed iterative scheme our results improve and extend the results announced by ceng and yao 2008 4

probability and time trade off probability and time are integral dimensions of virtually any decision to treat them together we consider the prospect of receiving outcome x with a probability p at time t we define risk and time distance and show that if these two distances are traded off linearly then preferences are characterized by three functions a value function a probability discount rate function and a psychological distance function the concavity of the psychological distance function explains the common ratio and common difference effects a decreasing probability discount rate accounts for the magnitude effect the discount rate and the risk premium depend on the shape of these three functions this paper was accepted by peter wakker decision analysis

the constrained newton method on a lie group and the symmetric eigenvalue problem the newton method for estimating a critical point of a real function is formulated in a coordinate free manner on an arbitrary lie group convergence proofs for the numerical method are given an application of the general approach to computing the eigenvalues of a symmetric matrix is given and the resultant algorithm is compared with the classical shifted qr algorithm properties of the method described suggest that it is of interest for certain computations in online and adaptive environments

a new method for solving equilibrium problem fixed point problem and variational inequality problem with application to optimization abstract in this paper we introduce a new iterative scheme for finding a common element of the set of solutions of an equilibrium problem the set of common fixed point for a family of infinitely nonexpansive mappings and the set of solutions of the variational inequality for inverse strongly monotone mappings in a hilbert space under suitable conditions some strong convergence theorems for approximating a common element of the above three sets are obtained as applications at the end of the paper we utilize our results to study the optimization problem and some convergence problem for strictly pseudocontractive mappings the results presented in the paper extend and improve some recent results of yao and yao y y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings appl math comput 186 2 2007 1551 1558 plubtieng and punpaeng s plubtieng r punpaeng a new iterative method for equilibrium problems and fixed point problems of nonlinear mappings and monotone mappings appl math comput 2007 doi 10 1016 j amc 2007 07 075 s takahashi and w takahashi s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2006 506 515 su shang and qin y f su m j shang x l qin an iterative method of solution for equilibrium and optimization problems nonlinear anal 2007 doi 10 1016 j na 2007 08 045 and chang cho and kim s s chang y j cho j k kim approximation methods of solutions for equilibrium problem in hilbert spaces dynam systems appl in print

equilibrium problems on riemannian manifolds with applications abstract we study equilibrium problem on general riemannian manifolds focusing on existence of solutions and the convexity properties of the solution set our approach consists in relating the equilibrium problem to a suitable variational inequality problem on riemannian manifolds and is completely different from previous ones on this topic in the literature we apply our results to the mixed variational inequality and the nash equilibrium problem moreover we formulate and analyze the convergence of the proximal point algorithm for the equilibrium problem in particular correct proofs are provided for the results claimed in j math anal appl 388 2012 61 77 i e theorems 3 5 and 4 9 there regarding the existence of the mixed variational inequality and the domain of the resolvent for the equilibrium problem on hadamard manifolds

nonlinear proximal point algorithms using bregman functions with applications to convex programming a bregman function is a strictly convex differentiable function that induces a well behaved distance measure or d function on euclidean space this paper shows that for every bregman function there exists a nonlinear version of the proximal point algorithm and presents an accompanying convergence theory applying this generalization of the proximal point algorithm to convex programming one obtains the d function proximal minimization algorithm of censor and zenios and a wide variety of new multiplier methods these multiplier methods are different from those studied by kort and bertsekas and include nonquadratic variations on the proximal method of multipliers

the amount based deformation of the q exponential discount function a joint analysis of delay and magnitude effects abstract the magnitude effect is one of the main anomalies shown by people in the context of intertemporal choice thus the main objective of this paper is to provide a general procedure to obtain a general discount function able to explain this paradox by this methodology we will to mathematically deform time in a discount function more specifically to multiply the variable time by a certain power of the reward amount however in most cases the existing literature presents some ad hoc discounting models to describe a unique anomaly in order to solve this limitation we will apply the former methodology to the q exponential discount function introduced by cajueiro 2006 in this way we will obtain a mathematical setting able to jointly explain the delay and the magnitude effects depending on the values of parameters q and involved in the model moreover another advantage of this amount based q exponential function is its convergence to the time deformed exponential hyperbolic and linear discounting depending on the value of q in the joint interval 1 1

a general iterative method for equilibrium problems and fixed point problems in hilbert spaces abstract in this paper we introduce two iterative schemes by the general iterative method for finding a common element of the set of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space then we prove two strong convergence theorems for nonexpansive mappings to solve a unique solution of the variational inequality which is the optimality condition for the minimization problem these results extended and improved the corresponding results of marino and xu g marino h k xu a general iterative method for nonexpansive mapping in hilbert spaces j math anal appl 318 2006 43 52 s takahashi and w takahashi s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 1 2007 506 515 and many others

on generalized equilibrium points generalizations of the usual definition of saddle point and equilibrium point are introduced in this paper the existence of these points is shown to be related to a class of functions that we call perturbed convex functions first and second order conditions regarding the existence of these points are also proved

existence and iteration for a mixed equilibrium problem and a countable family of nonexpansive mappings in banach spaces we prove the existence of a solution of the mixed equilibrium problem mep by using the kkm mapping in a banach space setting then by virtue of this result we construct a hybrid algorithm for finding a common element in the solutions set of a mixed equilibrium problem and the fixed points set of a countable family of nonexpansive mappings in the frameworks of banach spaces by using a projection technique we also prove that the sequences generated by the hybrid algorithm converge strongly to a common element in the solutions set of mep and common fixed points set of nonexpansive mappings moreover some applications concerning the equilibrium and the convex minimization problems are obtained

existence theorems for generalized noncoercive equilibrium problems the quasi convex case we provide a characterization of the nonemptiness of the solution set for generalized noncoercive equilibrium problems an extension of generalized quasi variational inequalities defined in reflexive banach spaces in the quasi convex case in addition several necessary and sufficient conditions for the set of solutions to these problems to be nonempty and bounded are also given our approach is based on recession notions which proved to be very useful in the study of noncoercive minimization problems in fact we find some particular cones as estimates for the recession cone of the solution set these cones for the ones containing the latter set are proved to be sharp enough to encompass several special situations found in the literature

ekeland s variational principle for vectorial multivalued mappings in a uniform space abstract in this paper we establish ekeland s variational principle and an equilibrium version of ekeland s variational principle for vectorial multivalued mappings in the setting of separated sequentially complete uniform spaces our approaches and results are different from those in chen et al 2008 hamel 2005 and lin and chuang 2010 13 14 15 as applications of our results we study vectorial caristi s fixed point theorems and takahashi s nonconvex minimization theorems for multivalued mappings and their equivalent forms in a separated sequentially complete uniform space we also apply our results to study maximal element theorems which are unified methods of several variational inclusion problems our results contain many known results in the literature fang 1996 21 and will have many applications in nonlinear analysis

vector valued perturbed equilibrium problems the goal of this paper is to prove some general vector valued perturbed equilibrium principles and some existence results of vector equilibrium points for bifunctions satisfying a new natural notion of lower semi continuity we obtain these results by going through a new concept of approximative equilibrium point

existence of equilibria via ekeland s principle abstract in the literature when dealing with equilibrium problems and the existence of their solutions the most used assumptions are the convexity of the domain and the generalized convexity and monotonicity together with some weak continuity assumptions of the function in this paper we focus on conditions that do not involve any convexity concept neither for the domain nor for the function involved starting from the well known ekeland s theorem for minimization problems we find a suitable set of conditions on the function f that lead to an ekeland s variational principle for equilibrium problems via the existence of e solutions we are able to show existence of equilibria on general closed sets for equilibrium problems and systems of equilibrium problems

on some nonlinear problems induced by an abstract maximal element principle abstract in this paper by applying an abstract maximal element principle on quasi ordered sets established by lin and du we obtain a generalized brezis browder principle system vectorial versions of ekeland s variational principle and maximal element principle and a vectorial version of takahashi s nonconvex minimization theorem moreover we investigate the equivalence between scalar versions and vectorial versions of these results

strong convergence theorems for solving equilibrium problems and fixed point problems of ξ strict pseudo contraction mappings by two hybrid projection methods in this paper we introduce an iterative scheme by using the hybrid projection methods for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a x strict pseudo contraction mapping in hilbert spaces we obtain two strong convergence theorems under mild assumptions on parameters for the sequences generated by these processes the results presented in the paper extend and improve some recent results of marino and xu g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 346 tada and takahashi a tada w takahashi weak and strong convergence theorems for a nonexpansive mapping and an equilibrium problem j optim theory appl 133 2007 359 370 and ceng et al l c ceng s al homidan q h ansari j c yao an iterative scheme for equilibrium problems and fixed point problems of strict pseudo contraction mappings j comput appl math 223 2009 967 974 and many others

equilibrium problems in hadamard manifolds abstract an equilibrium theory is developed in hadamard manifolds the existence of equilibrium points for a bifunction is proved under suitable conditions and applications to variational inequality fixed point and nash equilibrium problems are provided the convergence of picard iteration for firmly nonexpansive mappings along with the definition of resolvents for bifunctions in this setting is used to devise an algorithm to approximate equilibrium points

variational inequalities for set valued vector fields on riemannian manifolds convexity of the solution set and the proximal point algorithm we consider variational inequality problems for set valued vector fields on general riemannian manifolds the existence results of the solution convexity of the solution set and the convergence property of the proximal point algorithm for the variational inequality problems for set valued mappings on riemannian manifolds are established applications to convex optimization problems on riemannian manifolds are provided

discrete approximation of the radial contribution to the schrodinger time evolution operator in three dimensional euclidean space the laplace operator 2 on n dimensional euclidean space in spherical coordinates is the free particle schr dinger time evolution operator may be constructed by exponentiation denoting a central finite difference approximation of r by the matrix with is investigated and explicitly evaluated for n 3 provides an approximation of the leading term of the radial component of the kinetic energy contribution to the evolution operator an unconditionally stable numerical algorithm for quantum mechanical scattering is proposed based on this approximation when n 3

an iterative method of solution for equilibrium and optimization problems abstract in this paper we introduce an iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping the set of solutions of the variational inequality for an inverse strongly monotone mapping and the set of solutions of an equilibrium problem in a hilbert space we show that the iterative sequence converges strongly to a common element of the three sets the results of this paper extended and improved the results of h iiduka and w takahashi strong convergence theorems for nonexpansive mappings and inverse strongly monotone mappings nonlinear anal 61 2005 341 350 and s takahashi and w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 therefore by using the above result an iterative algorithm for the solution of a optimization problem was obtained

new existence results for equilibrium problems we consider equilibrium problems in the framework of the formulation proposed by blum and oettli which includes variational inequalities nash equilibria in noncooperative games and vector optimization problems for instance as particular cases we establish new sufficient and or necessary conditions for existence of solutions of such problems our results are based upon the relation between equilibrium problems and certain auxiliary convex feasibility problems together with extensions to equilibrium problems of gap functions for variational inequalities then we apply our results to some particular instances of equilibrium problems obtaining results which include among others a new lemma of the alternative for convex optimization problems

the multiplier penalty method for generalized nash equilibrium problems in banach spaces this paper deals with generalized nash equilibrium problems gneps in banach spaces we give an existence result for normalized equilibria of jointly convex gneps and then propose an augmented lag

partial proximal minimization algorithms for convex pprogramming an extension of the proximal minimization algorithm is considered where only some of the minimization variables appear in the quadratic proximal term the resulting iterates are interpreted in terms of the iterates of the standard algorithm and a uniform descent property is shown that holds independently of the proximal terms used this property is used to give simple convergence proofs of parallel algorithms where multiple processors simultaneously execute proximal iterations using different partial proximal terms it is also shown that partial proximal minimization algorithms are dual to multiplier methods with partial elimination of constraints and a relation is established between parallel proximal minimization algorithms and parallel constraint distribution algorithms

viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces abstract in this paper we introduce an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space then we prove a strong convergence theorem which is connected with combettes and hirstoaga s result p l combettes s a hirstoaga equilibrium programming in hilbert spaces j nonlinear convex anal 6 2005 117 136 and wittmann s result r wittmann approximation of fixed points of nonexpansive mappings arch math 58 1992 486 491 using this result we obtain two corollaries which improve and extend their results

multiplicative iterative algorithms for convex programming abstract we study multiplicative iterative algorithms for the minimization of a differentiable convex function defined on the positive orthant of r n if the objective function has compact level sets and has a locally lipschitz continuous gradient then these algorithms converge to a solution of the minimization problem moreover the convergence is nearly monotone in the sense of kullback leibler divergence special cases of these algorithms have been applied in position emission tomography and are formally related to the em algorithm for position emission tomography

a viscosity approximation scheme for system of equilibrium problems nonexpansive mappings and monotone mappings abstract in this paper we introduce a new viscosity approximation scheme based on the extragradient method for finding a common element of the set of solutions to a system of equilibrium problems the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions to the variational inequality for a monotone lipschitz continuous mapping several convergence results for the sequences generated by these processes in hilbert spaces were derived

equilibrium programming using proximal like algorithms we compute constrained equilibria satisfying an optimality condition important examples include convex programming saddle problems noncooperative games and variational inequalities under a monotonicity hypothesis we show that equilibrium solutions can be found via iterative convex minimization in the main algorithm each stage of computation requires two proximal steps possibly using bregman functions one step serves to predict the next point the other helps to correct the new prediction to enhance practical applicability we tolerate numerical errors

weak sharp minima on riemannian manifolds this is the first paper dealing with the study of weak sharp minima for constrained optimization problems on riemannian manifolds which are important in many applications we consider the notions of local weak sharp minima boundedly weak sharp minima and global weak sharp minima for such problems and establish their complete characterizations in the case of convex problems on finite dimensional riemannian manifolds and hadamard manifolds a number of the results obtained in this paper are also new for the case of conventional problems in finite dimensional euclidean spaces our methods involve appropriate tools of variational analysis and generalized differentiation on riemannian and hadamard manifolds developed and efficiently implemented in this paper

a new fourth order fourier bessel split step method for the extended nonlinear schrodinger equation fourier split step techniques are often used to compute soliton like numerical solutions of the nonlinear schrodinger equation here a new fourth order implementation of the fourier split step algorithm is described for problems possessing azimuthal symmetry in 3 1 dimensions this implementation is based in part on a finite difference approximation fda of 1 r r r r that possesses an associated exact unitary representation of e i 2 fda the matrix elements of this unitary matrix are given by special functions known as the associated bessel functions hence the attribute fourier bessel for the method the fourier bessel algorithm is shown to be unitary and unconditionally stable the fourier bessel algorithm is employed to simulate the propagation of a periodic series of short laser pulses through a nonlinear medium this numerical simulation calculates waveform intensity profiles in a sequence of planes that are transverse to the general propagation direction and labeled by the cylindrical coordinate z these profiles exhibit a series of isolated pulses that are offset from the time origin by characteristic times and provide evidence for a physical effect that may be loosely termed normal mode condensation normal mode condensation is consistent with experimentally observed pulse filamentation into a packet of short bursts which may occur as a result of short intense irradiation of a medium

on maximal element theorems variants of ekeland s variational principle and their applications abstract in this paper we establish several different versions of generalized ekeland s variational principle and maximal element theorem for functions in complete metric spaces the equivalence relations between maximal element theorems generalized ekeland s variational principle generalized caristi s common fixed point theorems and nonconvex maximal element theorems for maps are also proved moreover we obtain some applications to a nonconvex minimax theorem nonconvex vectorial equilibrium theorems and convergence theorems in complete metric spaces

the schauder fixed point theorem in geodesic spaces abstract we give a direct proof of schauder s fixed point theorem in the setting of geodesic metric spaces generalizing the classical schauder s theorem and improving a recent version of this theorem in cat spaces as an application we prove an existence result for a variational inequality in the setting of cat spaces

weak and strong convergence theorems for countable lipschitzian mappings and its applications abstract we use mann s iteration and the hybrid method in mathematical programming to obtain weak and strong convergence to common fixed points of a countable family of lipschitzian mappings finally we apply our results to solve the equilibrium problems and variational inequalities for continuous monotone mappings

variational inequalities on hadamard manifolds the notion of variational inequalities is extended to hadamard manifolds and related to geodesic convex optimization problems existence and uniqueness theorems for variational inequalities on hadamard manifolds are proved a convexity property of the solution set of a variational inequality on a hadamard manifold is presented

existence and stability of solutions for maximal element theorem on hadamard manifolds with applications abstract in this paper maximal element theorem on hadamard manifolds is established first we prove the existence of solutions for maximal element theorem on hadamard manifolds further we prove that most of problems in maximal element theorem on hadamard manifolds in the sense of baire category are essential and that for any problem in maximal element theorem on hadamard manifolds there exists at least one essential component of its solution set as applications we study existence and stability of solutions for variational relation problems on hadamard manifolds and existence and stability of weakly pareto nash equilibrium points for n person multi objective games on hadamard manifolds

convergence analysis of a proximal like minimization algorithm using bregman functions an alternative convergence proof of a proximal like minimization algorithm using bregman functions recently proposed by censor and zenios is presented the analysis allows the establishment of a global convergence rate of the algorithm expressed in terms of function values

an iterative scheme for equilibrium problems and fixed point problems of strict pseudo contraction mappings in this paper we propose an iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a strict pseudo contraction mapping in the setting of real hilbert spaces we establish some weak and strong convergence theorems of the sequences generated by our proposed scheme our results combine the ideas of marino and xu s result g marino h k xu weak and strong convergence theorems for strict pseudo contractions in hilbert spaces j math anal appl 329 2007 336 346 and takahashi and takahashi s result s takahashi w takahashi viscosity approximation methods for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 331 2007 506 515 in particular necessary and sufficient conditions for strong convergence of our iterative scheme are obtained

approximation theorems for solving common solution of a system of mixed equilibrium problems and variational inequality problems and fixed point problems for asymptotically strict pseudocontractions in the intermediate sense abstract in this paper we introduce a new iterative algorithm which is constructed by using the hybrid projection method for finding the common solution of a system of mixed equilibrium problems of bifunctions satisfying certain the conditions and the common solution of variational inequality problems of inverse strongly monotone mappings and the common solution of fixed point problems for a family of uniformly lipschitzian continuous and asymptotically i strict pseudocontractive mapping in the intermediate sense we prove the strong convergence theorem for a new iterative algorithm under some mild conditions in hilbert spaces finally we also give some numerical examples for support our results

newton methods for nonsmooth convex minimization connections among lagrangian riemannian newton and sqp methods this paper studies newton type methods for minimization of partly smooth convex functions sequential newton methods are provided using local parameterizations obtained from lagrangian theory and from riemannian geometry the hessian based on the lagrangian depends on the selection of a dual parameter g by revealing the connection to riemannian geometry a natural choice of g emerges for which the two newton directions coincide this choice of g is also shown to be related to the least squares multiplier estimate from a sequential quadratic programming sqp approach and with this multiplier sqp gives the same search direction as the newton methods

mixed equilibrium problems and optimization problems in this paper we introduce and analyze a new hybrid iterative algorithm for finding a common element of the set of solutions of mixed equilibrium problems and the set of fixed points of an infinite family of nonexpansive mappings furthermore we prove some strong convergence theorems for the hybrid iterative algorithm under some mild conditions we also discuss some special cases results obtained in this paper improve the previously known results in this area

variational convergence of bifunctions motivating applications it is shown that a number of variational and equilibrium problems can be cast as finding the maxinf points or minsup points of bivariate functions for short bifunctions these problems include linear and nonlinear complementarity problems fixed points variational inequalities inclusions noncooperative games and walras and nash equilibrium problems one appeals to the theory of lopsided convergence for bifunctions to derive stability results for each one of these problems

a douglas rachford splitting method for solving equilibrium problems abstract we propose a splitting method for solving equilibrium problems involving the sum of two bifunctions satisfying standard conditions we prove that this problem is equivalent to find a zero of the sum of two appropriate maximally monotone operators under a suitable qualification condition our algorithm is a consequence of the douglas rachford splitting applied to this auxiliary monotone inclusion connections between monotone inclusions and equilibrium problems are studied

associated bessel functions and the discrete approximation of the free particle time evolution operator in cylindrical coordinates a central finite difference approximation for the radial contribution r to the laplacian 2 r r r is considered in a three dimensional cylindrical coordinate system r z a free particle schrodinger time evolution operator is constructed by exponentiation e i 2 2 e 1 2 2 r r r e i 2 r r e i 2 r e i 2 r denoting the central finite difference approximation of r by 1 r2 t the matrix s e i 2 t with r2 is shown to be similar to a particular unitary representation uvk of the group of motions on euclidean three space that has been described by vilenkin and klimyk the matrix elements of uvk generalize the bessel function and provide an approximation of the leading term in the radial contribution to the evolution operator

strongly convergent algorithms by using new adaptive regularization parameter for equilibrium problems abstract two new algorithms are proposed in this paper for solving an equilibrium problem whose associated bifunction is monotone and satisfies a lipschitz type condition in a hilbert space in the first algorithm it is assumed that the value of the lipschitz constant of the bifunction is known while in the second one the prior knowledge of this constant is not explicitly requested the proposed algorithms are constructed around the proximal like mapping and the regularized method and use some new variable stepsize rules strong convergence theorems are established under some mild conditions imposed on bifunction and control parameters finally several numerical results are provided to illustrate the behavior of the new algorithms and to compare them to well known algorithms

iterative schemes for computing fixed points of nonexpansive mappings in banach spaces abstract let x be a real banach space with a normalized duality mapping uniformly norm to weak continuous on bounded sets or a reflexive banach space which admits a weakly continuous duality mapping j with gauge let f be an contraction and t n a sequence of nonexpansive mappings we study the strong convergence of explicit iterative schemes 1 x n 1 n f x n 1 n t n x n with a general theorem and then recover and improve some specific cases studied in the literature k aoyoma y kimura w takahashi m toyoda approximation of common fixed point of a countable family of nonexpansive mappings nonlinear anal 67 8 2007 2350 2360 g lopez v martin h k xu perturbation techniques for nonexpansive mappings with applications nonlinear anal real world appl in press available online 4 may 2008 h k xu viscosity approximation methods for nonexpansive mappings j math anal appl 298 1 2004 279 291 t h kim h k xu strong convergence of modified mann iterations nonlinear anal 61 1 2 2005 51 60 y song r chen strong convergence theorems on an iterative method for a family of finite nonexpansive mappings appl math comput 180 2006 275 287 y song r chen viscosity approximation methods for nonexpansive nonself mappings j math anal appl 321 1 2006 316 326 j chen l zhang t fan viscosity approximation methods for nonexpansive mappings and monotone mappings j math anal appl 334 2 2007 1450 1461 y kimura w takahashi m toyoda convergence to common fixed points of a finite family of nonexpansive mappings arch math 84 2005 350 363

a new iterative method for equilibrium problems and fixed point problems of nonexpansive mappings and monotone mappings abstract in this paper we introduce a new iterative scheme for finding the common element of the set of fixed points of a nonexpansive mapping the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for inverse strongly monotone mappings we show that the sequence converges strongly to a common element of the above three sets under some parameters controlling conditions this main theorem extends a recent result of yao and yao y yao j c yao on modified iterative method for nonexpansive mappings and monotone mappings applied mathematics and computation 186 2 2007 1551 1558

multivalued mixed variational inequalities with locally lipschitzian and locally cocoercive multivalued mappings abstract in this paper we study the problem of solving multivalued mixed variational inequalities by using some sequential approximation techniques of fixed point theory we solve the multivalued mixed variational inequalities involving locally lipschitzian or locally cocoercive multivalued mappings we establish that the convexity of the multivalued mapping values is not needed and construct by using the banach contraction principle converging sequences to the solutions also we show how to choose regularization parameters to compute these solutions

a note on the relevance of the q exponential function in the context of intertemporal choices abstract this paper shows that the q exponential function well known in the deformed algebra inspired in the tsallis s nonextensive thermodynamics may be used to model discount functions in intertemporal choices which present the phenomenon known as increasing patience moreover we show that this insight may also be used to provide a measure of the degree of dynamic inconsistency presented in such decisions

a dual view of equilibrium problems the aim of this paper is to introduce and study a dual problem associated to a generalized equilibrium problem gep we show that the solutions of gep and its dual are strictly related to the saddle points of an associated lagrangian function and under some suitable conditions to the solutions of a family of parametric optimization problems and their dual problems our results allow us to show that well known concepts and results from duality theory of some important particular cases of gep like variational inequalities and optimization problems can be recovered

local convergence of the proximal point method for a special class of nonconvex functions on hadamard manifolds abstract local convergence analysis of the proximal point method for a special class of nonconvex functions on hadamard manifold is presented in this paper the well definedness of the sequence generated by the proximal point method is guaranteed moreover it is proved that each cluster point of this sequence satisfies the necessary optimality conditions and under additional assumptions its convergence for a minimizer is obtained

strong convergence theorems for a countable family of quasi lipschitzian mappings and its applications abstract we use the hybrid method in mathematical programming to obtain strong convergence to common fixed points of a countable family of quasi lipschitzian mappings as a consequence several convergence theorems for quasi nonexpansive mappings and asymptotically strict pseudo contractions are deduced we also establish strong convergence of iterative sequences for finding a common element of the set of fixed point the set of solutions of an equilibrium problem and the set of solutions of a variational inequality with an appropriate setting we obtain the corresponding results due to tada takahashi and nakajo shimoji takahashi

a generalization of the q exponential discounting function abstract the aim of this paper is to generalize the q exponential discounting function introduced by cajueiro 2006 1 using the hyperbolic function as a base the presented generalization has two aspects first we consider any discounting function f t and not just hyperbolic discounting second the value of the parameter q is extended to the joint interval 1 1 in this way we have found a family of discounting functions whose elements are subadditive or superadditive according to the value of q

existence results for stampacchia and minty type implicit variational inequalities with multivalued maps abstract stampacchia and minty type generalized implicit variational inequality problems are considered we extended the notion of dense pseudomonotonicity for multivalued maps and established several existence results for solutions of these problems in the setting of segment dense sets we also studied the existence of solutions of minty type generalized implicit quasi variational inequality problems some particular cases are also studied it is shown that our results contain several existing results in the literature as special cases

on a generalized proximal point method for solving equilibrium problems in banach spaces abstract we introduce a regularized equilibrium problem in banach spaces involving generalized bregman functions for this regularized problem we establish the existence and uniqueness of solutions these regularizations yield a proximal like method for solving equilibrium problems in banach spaces we prove that the proximal sequence is an asymptotically solving sequence when the dual space is uniformly convex moreover we prove that all weak accumulation points are solutions if the equilibrium function is lower semicontinuous in its first variable we prove under additional assumptions that the proximal sequence converges weakly to a solution

a generalized distance and enhanced ekeland s variational principle for vector functions we propose a definition of lower closed transitive relations and prove the existence of minimal elements for such a relation this result is shown to contain probably a large part of existing versions of ekeland s variational principle evp we introduce the notion of a weak function p as a generalized distance and use it together with the above result on minimal elements to establish enhanced evp for various settings under relaxed lower semicontinuity assumptions these principles conclude the existence not only of p strict minimizers of p perturbations of the considered vector function but also p sharp and p strong minimizers our results are proved to be stronger than the classical evp and many generalizations in the literature even in the usual one dimensional case by numerous corollaries and examples we include equivalent formulations of our enhanced evp as well

on certain conditions for the existence of solutions of equilibrium problems the main purpose of this paper is the study of sufficient and or necessary conditions for existence of solutions of equilibrium problems we discuss some of the assumptions of the problem under which the introduced conditions are sufficient and or necessary and also analyze the effect of these assumptions on the connection between the solution sets of the equilibrium problem and of a related convex feasibility problem

vectorial form of ekeland type variational principle with applications to vector equilibrium problems and fixed point theory abstract this paper introduces a vectorial form of equilibrium version of ekeland type variational principle some equivalent results to our variational principle are given as applications we derive the existence of solutions of a vector equilibrium problem in the setting of complete quasi metric spaces with a w distance caristi kirk fixed point theorem for multivalued maps is also established in a more general setting

well posed equilibrium problems abstract in this paper we introduce some notions of well posedness for scalar equilibrium problems in complete metric spaces or in banach spaces as equilibrium problem is a common extension of optimization saddle point and variational inequality problems our definitions originates from the well posedness concepts already introduced for these problems we give sufficient conditions for two different kinds of well posedness and show by means of counterexamples that these have no relationship in the general case however together with some additional assumptions we show via ekeland s principle for bifunctions a link between them finally we discuss a parametric form of the equilibrium problem and introduce a well posedness concept for it which unifies the two different notions of well posedness introduced in the first part

ekeland s principle for vector equilibrium problems abstract in this paper the authors deal with bifunctions defined on complete metric spaces and with values in locally convex spaces ordered by closed convex cones the aim is to provide a vector version of ekeland s theorem related to equilibrium problems to prove this principle a weak notion of continuity of a vector valued function is considered and some of its properties are presented via the vector ekeland s principle existence results for vector equilibria are proved in both compact and noncompact domains

some generalizations of ekeland type variational principle with applications to equilibrium problems and fixed point theory abstract in this paper we introduce the concept of a q function defined on a quasi metric space which generalizes the notion of a function and a w distance we establish ekeland type variational principles in the setting of quasi metric spaces with a q function we also present an equilibrium version of the ekeland type variational principle in the setting of quasi metric spaces with a q function we prove some equivalences of our variational principles with caristi kirk type fixed point theorems for multivalued maps the takahashi minimization theorem and some other related results as applications of our results we derive existence results for solutions of equilibrium problems and fixed point theorems for multivalued maps we also extend the nadler s fixed point theorem for multivalued maps to a q function and in the setting of complete quasi metric spaces as a consequence we prove the banach contraction theorem for a q function and in the setting of complete quasi metric spaces the results of this paper extend and generalize many results appearing recently in the literature

iterative methods for solving systems of variational inequalities in reflexive banach spaces we prove strong convergence theorems for three iterative algorithms which approximate solutions to systems of variational inequalities for mappings of monotone type all the theorems are set in reflexive banach spaces and take into account possible computational errors

penalty methods for the solution of generalized nash equilibrium problems the generalized nash equilibrium problem gnep is an extension of the classical nash equilibrium problem where both the objective functions and the constraints of each player may depend on the rivals strategies this class of problems has a multitude of important engineering applications and yet solution algorithms are extremely scarce in this paper we analyze in detail a globally convergent penalty method that has favorable theoretical properties we also consider strengthened results for a particular subclass of problems very often considered in the literature basically our method reduces the gnep to a single penalized and nonsmooth nash equilibrium problem we suggest a suitable method for the solution of the latter penalized problem and present extensive numerical results

weak convergence theorem for monotone mappings and a countable family of nonexpansive mappings in this paper we introduce an iterative process for finding the common element of the set of common fixed points of a countable family of nonexpansive mappings and the set of solutions of the variational inequality problem for an a inverse strongly monotone mapping we obtain a weak convergence theorem for a sequence generated by this process moreover we apply our result to the problem for finding a common element of the set of equilibrium problems and the set of solutions of the variational inequality problem of a monotone mapping

a general iterative method for addressing mixed equilibrium problems and optimization problems abstract in this paper we introduce a new general iterative method for finding a common element of the set of solutions of a mixed equilibrium problem mep the set of fixed points of an infinite family of nonexpansive mappings t n n 1 and the set of solutions of variational inequalities for a inverse strongly monotone mapping in hilbert spaces furthermore we establish the strong convergence theorem for the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems our results extend and improve the recent results of yao et al y yao m a noor s zainab y c liou mixed equilibrium problems and optimization problems j math anal appl 354 2009 319 329 y yao m a noor y c liou on iterative methods for equilibrium problems nonlinear anal 70 1 2009 479 509 and many others

a tikhonov type regularization for equilibrium problems in hilbert spaces abstract in this paper we consider a general equilibrium problem in a hilbert space defined on a closed and convex set we show a tikhonov type regularization method that can be extended for the equilibrium problem under mild assumptions we establish the equivalence between the existence of solution of the original problem and the boundedness of the sequence generated by regularized problems

entropic proximal mappings with applications to nonlinear programming we introduce a family of new transforms based on imitating the proximal mapping of moreau and the associated moreau yosida proximal approximation of a function the transforms are constructed in terms of the a divergence functional a generalization of the relative entropy and of bregman s measure of distance an analogue of moreau s theorem associated with these entropy like distances is proved we show that the resulting entropic proximal maps share properties similar to the proximal mapping and provide a fairly general framework for constructing approximation and smoothing schemes for optimization problems applications of the results to the construction of generalized augmented lagrangians for nonlinear programs and the minimax problem are presented