new approximation schemes for general variational inequalities in this paper we suggest and consider a class of new three step approximation schemes for general variational inequalities our results include ishikawa and mann iterations as special cases we also study the convergence criteria of these schemes

on a class of nonconvex equilibrium problems in this paper we introduce a new class of equilibrium problems known as nonconvex equilibrium problems we suggest some algorithms for solving nonconvex equilibrium problems by using the auxiliary principle technique the convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomononicity we also introduce the concept of well posedness for the nonconvex equilibrium problems as special cases we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems our results can be considered a significant improvement of the previously known results

strong convergence theorems based on a new modified extragradient method for variational inequality problems and fixed point problems in banach spaces in this paper we introduce a new iterative algorithm by a modified extragradient method for finding a common element of the set of solutions of a general variational inequality and the set of common fixed points of an infinite family of k i strict pseudocontractions in a banach space we obtain some strong convergence theorems under suitable conditions the results obtained in this paper improve and extend the recent ones announced by many others

on iterative methods for equilibrium problems abstract in this paper we introduce a hybrid iterative scheme for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of finitely many nonexpansive mappings we prove that the approximate solution converges strongly to a solution of a class of variational inequalities under some mild conditions which is the optimality condition for some minimization problem we also give some comments on the results of plubtieng and punpaeng s plubtieng r punpaeng a general iterative method for equilibrium problems and fixed point problems in hilbert spaces j math anal appl 336 2007 455 469 results obtained in this paper may be viewed as an improvement and refinement of the previously known results in this area

parametric well posedness for variational inequalities defined by bifunctions in this paper we introduce the concepts of parametric well posedness for stampacchia and minty variational inequalities defined by bifunctions we establish some metric characterizations of parametric well posedness under suitable conditions we prove that the parametric well posedness is equivalent to the existence and uniqueness of solutions to these variational inequalities

simple dependent pairs of exponential and uniform random variables the accurate characterization of input processes for simulation models can require the representation of dependencies among input values results are presented on the generation of dependent exponential and uniform pairs of random variates a random coefficient linear function of two independent exponential variables yielding a third exponential variable is used in the construction of simple dependent pairs of exponential variables to model negative dependency the constructions employ antithetic exponential variables by employing negative exponentiation the constructions yield simple multiplicative based models for dependent uniform pairs the ranges of dependency allowable in the models are assessed by correlation calculations both of the product moment and spearman types broad ranges within the theoretically allowable ranges are found because of their simplicity all models are particularly suitable for simulation and are free of point and line concentrations of probabilities

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

co coercivity and its role in the convergence of iterative schemes for solving variational inequalities this paper stresses the role of co coercivity and related notions in the convergence of iterative schemes for solving monotone but not necessarily strongly or even strictly monotone variational inequalities the analysis will be conducted within the conceptual framework of the auxiliary problem principle

variational inequalities with generalized monotone operators we investigate the variational inequality with pseudomonotone operators in the sense of karamardian in banach spaces new existence results which extend many known results in infinite dimensional spaces are derived under rather weak assumptions new uniqueness results which also seem to be new even in finite dimensional spaces are also derived in particular new existence and uniqueness results for the complementarity problem with pseudomonotone operators in banach spaces are obtained also existence and uniqueness results for minimization problems with pseudoconvex functions in banach spaces are obtained

viscosity approximation methods for nonexpansive mappings abstract viscosity approximation methods for nonexpansive mappings are studied consider a nonexpansive self mapping t of a closed convex subset c of a banach space x suppose that the set fix t of fixed points of t is nonempty for a contraction f on c and t 0 1 let x t c be the unique fixed point of the contraction x tf x 1 t tx consider also the iteration process x n where x 0 c is arbitrary and x n 1 n f x n 1 n tx n for n 1 where n 0 1 if x is either hilbert or uniformly smooth then it is shown that x t and under certain appropriate conditions on n x n converge strongly to a fixed point of t which solves some variational inequality

multivalued general equilibrium problems in this paper we use the auxiliary principle technique to suggest some new classes of iterative algorithms for solving multivalued equilibrium problems the convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity as special cases we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems since multivalued equilibrium problems include equilibrium variational inequality and complementarity problems as specials cases our results continue to hold for these problems

on modified iterative method for 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 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 two sets under some parameters controlling conditions

on nonconvex equilibrium problems in this paper we introduce a new class of equilibrium problems known as mixed quasi nonconvex equilibrium problems we suggest some iterative schemes for solving nonconvex equilibrium problems by using the auxiliary principle technique the convergence of the proposed methods either requires partially relaxed strongly monotonicity or pseudomonotonicity as special cases we obtain a number of known and new results for solving various classes of equilibrium and variational inequality problems

some new algorithms for solving mixed equilibrium problems in this paper we suggest and analyze two projection methods one implicit and one explicit for finding a particular solution of a mixed equilibrium problem in a real hilbert space furthermore we prove that the proposed projection methods converge strongly to a particular solution of the mixed equilibrium problem

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

strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a hilbert space abstract we introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a hilbert space and then obtain that the sequence converges strongly to a common element of two sets using this result we prove three new strong convergence theorems in fixed point problems variational inequalities and equilibrium problems

hybrid algorithm for generalized mixed equilibrium problems and variational inequality problems and fixed point problems in this paper we introduce a new iterative algorithm by hybrid method for finding a common element of the set of solutions of finite general mixed equilibrium problems and the set of solutions of a general variational inequality problem for finite inverse strongly monotone mappings and the set of common fixed points of infinite family of strictly pseudocontractive mappings in a real hilbert space then we prove strong convergence of the scheme to a common element of the three above described sets our result improves and extends the corresponding results announced by many others

some developments in general variational inequalities general variational inequalities provide us with a unified natural novel and simple framework to study a wide class of equilibrium problems arising in pure and applied sciences in this paper we present a number of new and known numerical techniques for solving general variational inequalities using various techniques including projection wiener hopf equations updating the solution auxiliary principle inertial proximal penalty function dynamical system and well posedness we also consider the local and global uniqueness of the solution and sensitivity analysis of the general variational inequalities as well as the finite convergence of the projection type algorithms our proofs of convergence are very simple as compared with other methods our results present a significant improvement of previously known methods for solving variational inequalities and related optimization problems since the general variational inequalities include quasi variational inequalities and quasi implicit complementarity problems as special cases results presented here continue to hold for these problems several open problems have been suggested for further research in these areas

some aspects of variational inequalities abstract in this paper we provide an account of some of the fundamental aspects of variational inequalities with major emphasis on the theory of existence uniqueness computational properties various generalizations sensitivity analysis and their applications we also propose some open problems with sufficient information and references so that someone may attempt solution s in his her area of special interest we also include some new results which we have recently obtained

asymptotically non expansive self maps and global stability with ultimate boundedness of dynamic systems this paper investigates self maps t x x which satisfy a distance constraint in a metric space with mixed point dependent non expansive properties or in particular contractive ones and potentially expansive properties related to some distance threshold the above mentioned constraint is feasible in certain real world problems of usefulness for instance when discussing ultimate boundedness in dynamic systems which guarantees lyapunov stability this fact makes the proposed analysis to be potentially useful to investigate global stability properties in dynamic systems in the potential presence of some locally unstable equilibrium points the results can be applied to stability problems of dynamics systems and circuit theory as the given examples suggest

an iterative algorithm for approximating convex minimization problem we suggest and analyze an iterative algorithm without the assumption of any type of commutativity on an infinite family of nonexpansive mappings we show that the proposed iterative algorithm converges to the unique minimizer of some quadratic function over the common fixed point sets of an infinite family of nonexpansive mappings our result extend and improve many results announced by many authors

epidemic processes over adaptive state dependent networks in this paper we study the dynamics of epidemic processes taking place in adaptive networks of arbitrary topology we focus our study on the adaptive susceptible infected susceptible asis model where healthy individuals are allowed to temporarily cut edges connecting them to infected nodes in order to prevent the spread of the infection in this paper we derive a closed form expression for a lower bound on the epidemic threshold of the asis model in arbitrary networks with heterogeneous node and edge dynamics for networks with homogeneous node and edge dynamics we show that the resulting lower bound is proportional to the epidemic threshold of the standard sis model over static networks with a proportionality constant that depends on the adaptation rates furthermore based on our results we propose an efficient algorithm to optimally tune the adaptation rates in order to eradicate epidemic outbreaks in arbitrary networks we confirm the tightness of the proposed lower bounds with several numerical simulations and compare our optimal adaptation rates with popular centrality measures