convergence and certain control conditions for hybrid viscosity approximation methods abstract very recently yao chen and yao 20 proposed a hybrid viscosity approximation method which combines the viscosity approximation method and the mann iteration method under the convergence of one parameter sequence to zero they derived a strong convergence theorem in a uniformly smooth banach space in this paper under the convergence of no parameter sequence to zero we prove the strong convergence of the sequence generated by their method to a fixed point of a nonexpansive mapping which solves a variational inequality an appropriate example such that all conditions of this result are satisfied and their condition n 0 is not satisfied is provided furthermore we also give a weak convergence theorem for their method involving a nonexpansive mapping in a hilbert space

strong convergence theorems by hybrid methods for families of nonexpansive mappings in hilbert spaces abstract in this paper we prove a strong convergence theorem by the hybrid method for a family of nonexpansive mappings which generalizes nakajo and takahashi s theorems k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 simultaneously furthermore we obtain another strong convergence theorem for the family of nonexpansive mappings by a hybrid method which is different from nakajo and takahashi using this theorem we get some new results for a single nonexpansive mapping or a family of nonexpansive mappings in a hilbert space

strong convergence of modified mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space we propose two modifications of the mann iterations in a uniformly smooth banach space one for nonexpansive mappings and the other for the resolvent of accretive operators the two modified mann iterations are proved to have strong convergence

a fast ell 1 tv algorithm for image restoration image restoration problems are often solved by finding the minimizer of a suitable objective function consisting of a data fitting term and a regularization term in this paper we consider the data fitting term measured in the ell 1 norm to handle non gaussian additive noise and the regularization term given by the total variation tv to restore image edges we propose a new algorithm for this image restoration problem by making use of new variables to modify the data fitting term and the tv regularization term an alternating minimization method based on the new formulation is employed to restore blurred and noisy images our experimental results show that the quality of restored images by the proposed method is competitive with those restored by the other tested methods we also show the convergence of the alternating minimization algorithm and demonstrate that the proposed algorithm is very efficient

the ale method with triangular elements direct convection of integration point values the arbitrary lagrangian eulerian ale finite element method is applied to the simulation of forming processes where material is highly deformed here the split formulation is used a lagrangian step is done with an implicit finite element formulation followed by an explicit purely convective eulerian step the purpose of this study is to investigate the eulerian step for quadratic triangular elements to solve the convection equation for integration point values a new method inspired by van leer is constructed the new method is based on direct convection of integration point values without intervention of nodal point values the molenkamp test and a so called block test were executed to check the performance and stability of the convection scheme from these tests it is concluded that the new convection scheme shows accurate results the scheme is extended to an ale algorithm an extrusion process was simulated to test the applicability of the scheme to engineering problems it is concluded that direct convection of integration point values with the presented algorithm leads to accurate results and that it can be applied to ale simulations

shrinking projection methods for firmly nonexpansive mappings abstract the purpose of this paper is to study the shrinking projection method for firmly nonexpansive mappings the method gives us a strong convergence iteration for a family of firmly nonexpansive mappings and also permit us to obtain a sufficient condition for the existence of a fixed point of a firmly nonexpansive mapping

convergence of ishikawa s iteration method for pseudocontractive mappings let c be a nonempty closed and convex subset of a real hilbert space h let ti c c i 1 2 n be a finite family of lipschitz pseudocontractive mappings it is our purpose in this paper to prove strong convergence of ishikawa s method to a common fixed point of a finite family of lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty no compactness assumption is imposed either on t or on c moreover computation of the closed convex set cn for each n 1 is not required the results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings

strong convergence theorems for equilibrium problems and relatively nonexpansive mappings in banach spaces the purpose of the paper is to introduce modified halpern and ishikawa iteration for finding a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in banach spaces we also consider two strong convergence theorems for relatively nonexpansive mappings with some proper restriction

restoration of blurred color images with impulse noise restoration of images degraded by blurring and impulse noise has received considerable attention recently guo et al 2009 proposed a fast l 1 total variation algorithm for grayscale image restoration with impulse noise in this paper we extend their idea for deblurring color images with impulse noise an alternating iteration scheme is adopted for solving the corresponding problem more importantly we employ the five point property to analyze the convergence of the proposed alternating algorithm numerical experiments demonstrate that the proposed method could deblur color images with good quality

convergence of the modified mann s iteration method for asymptotically strict pseudo contractions abstract let c be a closed convex subset of a real hilbert space h and assume that t is an asymptotically strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the modified mann s algorithm generates a sequence x n via the formula x n 1 n x n 1 n t n x n n 0 it is proved that if the control sequence n is chosen so that n 1 for some 0 1 then x n converges weakly to a fixed point of t we also modify this iteration method by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strongly convergent sequence

analysis and application of a novel fast algorithm for 2 d arma model parameter estimation abstract in this paper we analyze a novel algorithm for 2 d arma model parameter estimation in the presence of noise and then develop a fast and efficient blind image restoration algorithm we show that the novel algorithm can minimize a quadratic convex optimization problem and has a lower computational complexity than the conventional algorithms as a result the novel algorithm involves no convergence and local minimum issue moreover the proposed blind image restoration algorithm can overcome the local minimization problem computed results confirm that the novel algorithm can more quickly obtain more accurate estimates than the conventional algorithms in the presence of noise

on some algorithms in banach spaces finding fixed points of nonlinear mappings abstract by using a modification of the hybrid method in mathematical programming we give some new algorithm to find out a fixed point of mappings which are in some sense non expansive our results hold in reflexive strictly convex smooth banach spaces with the kadec klee property

approximating fixed points of nonexpansive mappings in a banach space by metric projections abstract in this paper a strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth banach space is proved by using metric projections this theorem is different from the recent strong convergence theorem due to xu h k xu strong convergence of approximating fixed point sequences for nonexpansive mappings bull aust math soc 74 2006 143 151 which was established by generalized projections

convergence to common fixed point of nonexpansive semigroups let e be a uniformly convex banach space whose norm is uniformly gateaux differentiable c be closed convex subset of e s t s s 0 be a nonexpansive semigroup on c such that the set of common fixed points of t s s 0 is nonempty let f c c be a contraction a n b n t n be real sequences such that 0 a n 0 lim n b n 0 and lim n t n y 0 c in this paper we show that the two iterative sequence as follows x n a nf x n 1 a n 1t n 0 t nt s x nds y n 1 b nf y n 1 b n 1t n 0 t nt s y ndsconverge strongly to a common fixed point of t s s 0 which solves some variational inequality when a n b n satisfy some appropriate conditions

weak and strong convergence theorems for strict pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c with a fixed point for some 0 1 given an initial guess x 0 c and given also a real sequence n in 0 1 the mann s algorithm generates a sequence x n by the formula x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then x n converges weakly to a fixed point of t however this convergence is in general not strong we then modify mann s algorithm by applying projections onto suitably constructed closed convex sets to get an algorithm which generates a strong convergent sequence this result extends a recent result of nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 from nonexpansive mappings to strict pseudo contractions

a fast image recovery algorithm based on splitting deblurring and denoising in this paper we employ a popular splitting strategy to design a fast iterative algorithm for image restoration we divide the algorithm into two steps i e deblurring step and denoising step in the deblurring step fourier transform is employed for image deblurring under the periodic boundary condition in the denoising step we use a simple and fast method called fast iterative shrinkage thresholding algorithm fista to reduce image noise in addition we also give the convergence analysis for the proposed method visual and quantitative results demonstrate the proposed algorithm applied to l 1 regularization model and total variation tv regularization model is a faster algorithm and keeps image details well

realization of the hybrid method for mann iterations abstract the mann iterations for nonexpansive mappings have only weak convergence even in a hilbert space h in order to overcome this weakness nakajo and takahashi proposed the hybrid method for mann s iteration process x 0 c chosen arbitrarily y n n x n 1 n tx n c n z c y n z x n z q n z c x 0 x n z x n 0 x n 1 p c n q n x 0 n 0 1 2 where c is a nonempty closed convex subset of h t c c is a nonexpansive mapping and p k is the metric projection from h onto a closed convex subset k of h however it is difficult to realize this iteration process in actual computing programs because the specific expression of p c n q n x 0 cannot be got in general in the case where c h we obtain the specific expression of p c n q n x 0 and thus the hybrid method for mann s iteration process can be realized easily numerical results show advantages of our result

approximations for nonlinear mappings by the hybrid method in hilbert spaces abstract the hybrid method in mathematical programming was introduced by haugazeau 1968 1 and he proved a strong convergence theorem for finding a common element of finite nonempty closed convex subsets of a real hilbert space later bauschke and combettes 2001 2 proposed some condition for a family of mappings the so called coherent condition and established interesting results by the hybrid method the authors nakajo et al 2009 10 extended bauschke and combettes s results in this paper we introduce a condition weaker than the coherent condition and prove strong convergence theorems which generalize the results of nakajo et al 2009 10 and we get strong convergence theorems for a family of asymptotically strict pseudo contractions a family of lipschitz and pseudo contractive mappings and a one parameter uniformly lipschitz semigroup of pseudo contractive mappings

a hybrid algorithm for pseudo contractive mappings abstract in this paper we suggest and analyze a hybrid algorithm for pseudo contractive mappings in hilbert spaces further we prove the strong convergence of the proposed iterative algorithm for lipschitz pseudo contractive mappings in hilbert spaces

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

strong convergence of modified ishikawa iteration for two asymptotically nonexpansive mappings and semigroups abstract in this paper we established strong convergence theorems for a common fixed point of two asymptotically nonexpansive mappings and for a common fixed point of two asymptotically nonexpansive semigroups by using the hybrid method in a hilbert space moreover we also proved a strong convergence theorem for a common fixed point of two nonexpansive mappings our results extend and improve the recent ones announced by kim and xu t w kim h w xu strong convergence of modified mann iteration for asymptotically nonexpansive mappings and semigroups nonlinear anal 64 2006 1140 1152 nakajo and takahashi k nakajo w takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 and many others

convergence in norm of modified krasnoselski mann iterations for fixed points of demicontractive mappings abstract this paper deals with fixed points methods related to the general class of demicontractive mappings including the well known classes of nonexpansive and quasi nonexpansive mappings in hilbert spaces specifically we point out some historical aspects concerning the concept of demicontactivity and we investigate a regularized variant of the krasnoselski mann iteration that can be alternatively regarded as a simplified form of the inertial iteration p e mainge j math anal appl 344 2008 876 887 with non constant relaxation factors these two methods ensure the strong convergence of the generated sequence towards the least norm element of the set of fixed points of demicontractive mappings however for convergence our method does not require anymore the knowledge of some constant related to the involved demicontractive operator a new and simpler proof is also proposed for its convergence even when involving non constant relaxation factors we point out the simplicity of this algorithm at least from computational point of view in comparison with other existing methods we also present some numerical experiments concerning a convex feasibility problem experiments that emphasize the characteristics of the considered algorithm comparing with a classical cyclic projection type iteration

convergence of mann s type iteration method for generalized asymptotically nonexpansive mappings let c be a nonempty closed and convex subset of a real hilbert space h let t i c h i 1 2 n be a finite family of generalized asymptotically nonexpansive mappings it is our purpose in this paper to prove strong convergence of mann s type method to a common fixed point of t i i 1 2 n provided that the interior of common fixed points is nonempty no compactness assumption is imposed either on t or on c as a consequence it is proved that mann s method converges for a fixed point of nonexpansive mapping provided that interior of f t 0 the results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings

discrete time neural network for fast solving large linear l_ 1 estimation problems and its application to image restoration there is growing interest in solving linear l1 estimation problems for sparsity of the solution and robustness against non gaussian noise this paper proposes a discrete time neural network which can calculate large linear l1 estimation problems fast the proposed neural network has a fixed computational step length and is proved to be globally convergent to an optimal solution then the proposed neural network is efficiently applied to image restoration numerical results show that the proposed neural network is not only efficient in solving degenerate problems resulting from the nonunique solutions of the linear l1 estimation problems but also needs much less computational time than the related algorithms in solving both linear l1 estimation and image restoration problems

strong convergence of the modified mann iterative method for strict pseudo contractions in this paper we introduce a modified mann iterative process for approximating a common fixed point of a finite family of strict pseudo contractions in hilbert spaces we establish the strong convergence theorem of the general iteration scheme under some mild conditions our results extend and improve the recent ones announced by many others

strong convergence of mann s type iterations for nonexpansive semigroups in general banach spaces abstract in this paper we prove a strong convergence theorem of mann s type for commutative nonexpansive semigroups in general banach spaces using this theorem we obtain some strong convergence theorems in general banach spaces

strong convergence theorems for a finite family of asymptotically nonexpansive mappings and semigroups strong convergence theorems are obtained for a finite family of asymptotically nonexpansive mappings and semigroups by the modified mann method

strong convergence to common fixed points of families of nonexpansive mappings abstract we introduce iteration schemes for families of nonexpansive mappings in hilbert spaces and prove that the iterates converge strongly to common fixed points of the mappings

modified hybrid algorithms for lipschitz quasi pseudo contractive mappings in hilbert spaces in this paper strong convergence theorems are obtained by modified hybrid methods for lipschitz quasi pseudo contractions in a hilbert space besides applications of these theorems are introduced finally we use these methods to modify ishikawa s iteration process and get some strong convergence theorems which are different from zhou h y zhou convergence theorems of fixed points for lipschitz pseudo contractions in hilbert spaces j math anal appl 343 2008 546 556

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

locally implicit total variation diminishing schemes on unstructuredtriangular meshes a numerical solution procedure that includes locally implicit total variation diminishing schemes and adaptive mesh generation techniques has been developed in this work in a cartesian coordinate system the euler equations are solved by using a cell centered finite volume algorithm a new construction of symmetric total variation diminishing schemes on unstructured triangular meshes is presented the validation of the present solution adaptive methods is confirmed by comparison with related numerical results for inviscid flows around an isolated naca 0012 airfoil and passing through a channel with a circular arc bump in transonic and supersonic flow regimes to further prove the feasibility of this approach a two element airfoil flow is also investigated furthermore one unsteady transonic channel flow is studied to demonstrate the reliability and capability of the present solution procedure for a time accurate calculation

convergence theorems of common fixed points for a family of lipschitz quasi pseudocontractions abstract in an infinite dimensional hilbert space the normal mann s iteration has only weak convergence in general even for nonexpansive mappings the purpose of this paper is to modify the normal mann s iteration to have strong convergence for a family of lipschitz quasi pseudocontractions in the framework of hilbert spaces our results improve and extend the corresponding ones announced by many others

multiblock hybrid grid finite volume method to solve flow in irregular geometries in this work a finite volume based finite element method is suitably developed for solving incompressible flow and heat transfer on collocated hybrid grid topologies the method is generally applicable to arbitrarily shaped elements and orientations and thus challenges the potential to unify many of the different grid topologies into a single formulation the key point in this formulation is the correct estimation of the convective and diffusive fluxes at the cell faces using a novel physical influence scheme this scheme remarkably enhances the achieved solution accuracy it is shown that the extended formulation is robust enough to treat any combination of multiblock meshes with dual element shape employments in this regard the solution domain is broken up into a number of different multiblock arrangements in which each block is filled with only one type of finite element shape the combined grid can decrease the computational time and memory requirements and increase the numerical accuracy the results of the extended formulation are validated against different benchmark and other solutions the current results are in excellent agreement with the other solutions without exhibiting any disturbances around the block boundaries

positive weak solutions of semilinear second order elliptic inequalities via variational inequalities existence uniqueness and convergence of approximants of positive weak solutions for semilinear second order elliptic inequalities are obtained the nonlinearities involved in these inequalities satisfy suitable upper or lower bound conditions or monotonicity conditions the lower bound conditions are allowed to contain the critical sobolev exponents the methodology is to establish variational inequality principles for demicontinuous pseudo contractive maps in hilbert spaces by considering convergence of approximants and apply them to the corresponding variational inequalities arising from the semilinear second order elliptic inequalities examples on the existence uniqueness and convergence of approximants of positive weak solutions of the semilinear second order elliptic inequalities are given

on hybrid projection methods for asymptotically quasi φ nonexpansive mappings the purpose of this paper is to consider the problem of approximating a common fixed point of two asymptotically quasi f nonexpansive mappings based on hybrid projection methods strong convergence theorems are established in a real banach space

a duality based splitting method for ell 1 tv image restoration with automatic regularization parameter choice a novel splitting method is presented for the ell 1 tv restoration of degraded images subject to impulsive noise the functional is split into an ell 2 tv denoising part and an ell 1 ell 2 deblurring part the dual problem of the relaxed functional is smooth with convex constraints and can be solved efficiently by applying an arrow hurwicz type algorithm to the augmented lagrangian formulation the regularization parameter is chosen automatically based on a balancing principle the accuracy the fast convergence and the robustness of the algorithm and the use of the parameter choice rule are illustrated on some benchmark images and compared with an existing method

strong convergence for an implicit iteration process in hilbert spaces abstract in this paper we prove strong convergence theorems for the mann type implicit process of a continuous hemicontractive mappings defined on a noncompact domain in real hilbert spaces

t class algorithms for pseudocontractions and κ strict pseudocontractions in hilbert spaces in this paper we study iterative algorithms for finding a common element of the set of fixed points of strict pseudocontractions or finding a solution of a variational inequality problem for a monotone lipschitz continuous mapping the last problem being related to finding fixed points of pseudocontractions these algorithms were already studied in 1 and 9 but our aim here is to provide the links between these know algorithms and the general framework of t class algorithms studied in 3

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

high order tvl1 based images restoration and spatially adapted regularization parameter selection abstract the total variation tv model with an l 1 fidelity term tvl1 is a famous model to recover blurred and impulse noisy image with edges preserving however it usually causes some staircase effects in this paper we propose a hybrid model combining the tv regularizer and the high order tv regularizer with the tvl1 model htvl1 for blurred and salt and pepper impulse noisy image restoration the solving algorithm is under the frame work of alternating direction method of multipliers admm in addition a spatially adapted regularization parameter selection scheme is also used numerical results show that the quality of restored images by the proposed methods is competitive with the quality of restored images by some other existing methods

strong convergence of a new iterative scheme for a finite family of strict pseudo contractions the purpose of this paper is to introduce a new iterative scheme for finding a common fixed point of a finite family of strict pseudo contractions the results obtained in this paper extend and improve the corresponding results of marino colao qin and kang g marino v colao x qin s m kang strong convergence of the modified mann iterative method for strict pseudo contractions comput math appl 57 2009 455 465

an iterative method for equilibrium problems and a finite family of relatively nonexpansive mappings in a banach space abstract in this paper we introduce a new iterative method for finding a common element of the set of fixed points of a finite family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in uniformly convex and uniformly smooth banach spaces then we prove a strong convergence theorem by using the generalized projection

adaptive finite volume upwind approach on mixed quadrilateral triangular meshes an adaptive cell vertex finite volume upwind approach on unstructured mixed quadrilateral triangular meshes where the quadrilaterals are directionally stretched in the flow regions having one dimensional features has been developed to solve the unsteady euler equations in the present approach the runge kutta time integration roe s riemann solver muscl differencing with characteristic interpolation variables a new treatment of the rotated extrapolation boundary condition and a modified technique of the global local regeneration for directionally stretched meshes are included by using different combinations of interpolation variables limiter functions and numerical implementations of boundary conditions a systematic study is made to understand the characteristics of the current approach in this work the isolated oblique shock problem shock reflection at a wall supersonic flow passing through a channel with a 4 circular arc bump transonic flows around single and two element airfoils as well as the shock propagation in a channel are investigated it is concluded that the present solution procedure demonstrates good convergence performance and provides accurate and high resolution results for the steady and unsteady inviscid flows

iterative methods for the computation of fixed points of demicontractive mappings this paper surveys some of the main convergence properties of the mann type iteration for the demicontractive mappings some variants of the mann iteration that ensure the strong convergence like the cq algorithm and a variant for the asymptotically demicontractive mappings are also considered the usual framework of our study is a real hilbert space and only to a certain extent some particular banach spaces historical aspects are pointed out and some applications for the convex feasibility problem are discussed

viscosity approximations by the shrinking projection method in hilbert spaces we consider viscosity approximations by using the shrinking projection method established by takahashi takeuchi and kubota and the modified shrinking projection method proposed by qin cho kang and zhou for finding a common fixed point of countably many nonlinear mappings and we prove strong convergence theorems which extend some known results we also consider semigroups of nonlinear mappings and obtain strong convergence of iterative schemes which approximate a common fixed point of the semigroup under certain conditions

fast nonconvex nonsmooth minimization methods for image restoration and reconstruction nonconvex nonsmooth regularization has advantages over convex regularization for restoring images with neat edges however its practical interest used to be limited by the difficulty of the computational stage which requires a nonconvex nonsmooth minimization in this paper we deal with nonconvex nonsmooth minimization methods for image restoration and reconstruction our theoretical results show that the solution of the nonconvex nonsmooth minimization problem is composed of constant regions surrounded by closed contours and neat edges the main goal of this paper is to develop fast minimization algorithms to solve the nonconvex nonsmooth minimization problem our experimental results show that the effectiveness and efficiency of the proposed algorithms

degree of convergence of modified averaged iterations for fixed points problems and operator equations abstract let h be a real hilbert space we propose a modification for averaged mappings to approximate the unique fixed point of a mapping t h h such that t is boundedly lipschitzian and t is monotone we not only prove strong convergence theorems but also determine the degree of convergence using this result an iteration process is given for finding the unique solution of the equation a x f where a h h is strongly monotone and boundedly lipschitzian

an implicit iterative scheme for monotone variational inequalities and fixed point problems abstract in this paper we introduce an implicit iterative scheme for finding a common element of the set of common fixed points of n nonexpansive mappings and the set of solutions of the variational inequality problem for a monotone lipschitz continuous mapping the implicit iterative scheme is based on two well known methods extragradient and approximate proximal we obtain a weak convergence theorem for three sequences generated by this implicit iterative scheme on the basis of this theorem we also construct an implicit iterative process for finding a common fixed point of n 1 mappings such that one of these mappings is taken from the more general class of lipschitz pseudocontractive mappings and the other n mappings are nonexpansive

strong convergence of the cq method for fixed point iteration processes strong convergence theorems are obtained for the cq method for an ishikawa iteration process a contractive type iteration process for nonexpansive mappings and the proximal point algorithm for maximal monotone operators in hilbert spaces

convergence theorems of fixed points for lipschitz pseudo contractions in hilbert spaces abstract let c be a closed convex subset of a real hilbert space h and assume that t is a strict pseudo contraction on c consider mann s iteration algorithm given by x 0 c x n 1 n x n 1 n t x n n 0 it is proved that if the control sequence n is chosen so that n 1 and n 0 n 1 n then lim n x n t x n d 0 r a where a i t and d 0 d denotes the distance between the origin and the subset set d of h as a consequence of this result we prove that if t has a fixed point in c then x n converges weakly to a fixed point of t also we extend a result due to reich to strict pseudo contractions in the hilbert space setting further by virtue of hybridization projections we establish a strong convergence theorem for lipschitz pseudo contractions the results presented in this paper improve or extend the corresponding results of browder and petryshyn f e browder w v petryshyn construction of fixed points of nonlinear mappings in hilbert spaces j math anal appl 20 1967 197 228 rhoades b e rhoades fixed point iterations using infinite matrices trans amer math soc 196 1974 162 176 and 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 1 2007 336 346

strong convergence theorems obtained by a generalized projections hybrid method for families of mappings in banach spaces abstract let c be a nonempty closed and convex subset of a uniformly convex and smooth banach space and let t n be a family of mappings of c into itself such that the set of all common fixed points of t n is nonempty we consider a sequence x n generated by the hybrid method by generalized projection in mathematical programming we give conditions on t n under which x n converges strongly to a common fixed point of t n and generalize the results given in 12 14 13 11

strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in this paper we show strong convergence theorems for nonexpansive mappings and nonexpansive semigroups in hilbert spaces by the hybrid method in the mathematical programming

strong convergence theorem of an iterative method for variational inequalities and fixed point problems in hilbert spaces in this paper we introduce a new iteration method based on the hybrid method in mathematical programming and the descent like method for finding a common element of the set of solutions for a variational inequality and the set of fixed points for a nonexpansive mapping in hilbert spaces our method modifies and improves some methods in literature

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

new monotone hybrid algorithm for hemi relatively nonexpansive mappings and maximal monotone operators the purpose of this article is to prove the strong convergence theorems for hemi relatively nonexpansive mappings in banach spaces in order to get the strong convergence theorems for hemi relatively nonexpansive mappings a new monotone hybrid iteration algorithm is presented and is used to approximate the fixed point of hemi relatively nonexpansive mappings noting that the general hybrid iteration algorithm can be used for relatively nonexpansive mappings but it can not be used for hemi relatively nonexpansive mappings however this new monotone hybrid algorithm can be used for hemi relatively nonexpansive mappings in addition a new method of proof has been used in this article that is by using this new monotone hybrid algorithm we firstly claim that the iterative sequence is a cauchy sequence the results of this paper modify and improve the results of matsushita and takahashi and some others

strong convergence theorems for an infinite family of quasi nonexpansive mappings and generalized equilibrium problems and variational inequality problems in this paper we introduce a new iterative scheme for finding a common element of the set of common fixed points of an infinite family of uniformly continuous quasi nonexpansive mappings and the set of solutions to a generalized equilibrium problem and the set of solutions to a variational inequality problem in a real hilbert space we then prove strong convergence of the scheme to a common element of the three mentioned sets our results extend important recent results

strong convergence for a countable family of strict pseudocontractions in q uniformly smooth banach spaces we introduce a new iterative algorithm for finding a common fixed point of a countable family of strict pseudocontractions in q uniformly smooth and uniformly convex banach spaces we then prove that the sequence generated by the proposed algorithm converges strongly to a common fixed point of an infinite family of strict pseudocontractions our results mainly improve and extend the results announced by yao et al y yao y c liou g marino strong convergence of two iterative algorithms for nonexpansive mappings in hilbert spaces fixed point theory appl 2009 2009 7 pages doi 10 1155 2009 279058 art id 279058

strong convergence theorems for a family of lipschitz quasi pseudo contractions in hilbert spaces abstract the purpose of this paper is to propose several modified hybrid projection algorithms and prove several strong convergence theorems for common fixed points of a family of lipschitz quasi pseudo contractions in the framework of hilbert spaces the results presented in this paper improve and extend the corresponding ones announced by many others

iterative methods for strict pseudo contractions in hilbert spaces abstract let t i i 1 n be n strict pseudo contractions defined on a closed convex subset c of a real hilbert space h consider the problem of finding a common fixed point of these mappings and consider the parallel and cyclic algorithms for solving this problem we will prove the weak convergence of these algorithms moreover by applying additional projections we further prove that these algorithms can be modified to have strong convergence

implicit iterative algorithms for asymptotically nonexpansive mappings in the intermediate sense and lipschitz continuous monotone mappings in this paper we introduce some implicit iterative algorithms for finding a common element of the set of fixed points of an asymptotically nonexpansive mapping in the intermediate sense and the set of solutions of the variational inequality problem for a monotone lipschitz continuous mapping these implicit iterative algorithms are based on two well known methods extragradient and approximate proximal methods we obtain some weak convergence theorems for these implicit iterative algorithms based on these theorems we also construct some implicit iterative processes for finding a common fixed point of two mappings such that one of these two mappings is taken from the more general class of lipschitz pseudocontractive mappings and the other mapping is asymptotically nonexpansive

strong convergence of modified mann iterations for asymptotically nonexpansive mappings and semigroups abstract the mann iterations for nonexpansive mappings have in general only weak convergence in a hilbert space we modify an iterative method of mann s type introduced by nakajo and takahashi strong convergence theorems for nonexpansive mappings and nonexpansive semigroups j math anal appl 279 2003 372 379 for nonexpansive mappings and prove strong convergence of our modified mann s iteration processes for asymptotically nonexpansive mappings and semigroups

strong convergence theorems by halpern mann iterations for relatively nonexpansive mappings in banach spaces abstract in this paper we modify halpern and mann s iterations for finding a fixed point of a relatively nonexpansive mapping in a banach space consequently a strong convergence theorem for a nonspreading mapping is deduced using a concept of duality theorems we also obtain analogue results for certain generalized nonexpansive and generalized nonexpansive type mappings finally we discuss two strong convergence theorems concerning two types of resolvents of a maximal monotone operator in a banach space

blind deconvolution using generalized cross validation approach to regularization parameter estimation in this paper we propose and present an algorithm for total variation tv based blind deconvolution both the unknown image and blur can be estimated within an alternating minimization framework with the generalized cross validation gcv method the regularization parameters associated with the unknown image and blur can be updated in alternating minimization steps experimental results confirm that the performance of the proposed algorithm is better than variational bayesian blind deconvolution algorithms with student s t priors or a total variation prior

hybrid ishikawa iterative methods for a nonexpansive semigroup in hilbert space in this paper on the base of the ishikawa iteration method and the hybrid method in mathematical programming we give two new strong convergence methods for finding a point in the common fixed point set of a nonexpansive semigroup in hilbert space

approximation of common fixed points for a countable family of relatively nonexpansive mappings in a banach space and applications abstract in this paper we prove a strong convergence theorem by the hybrid method for a countable family of relatively nonexpansive mappings in a banach space we also establish a new control condition for the sequence of mappings t n which is weaker than the control condition in lemma 3 1 of aoyama et al k aoyama y kimura w takahashi and m toyoda approximation of common fixed points of a countable family of nonexpansive mappings in a banach space nonlinear anal 67 2007 2350 2360 moreover we apply our results for finding a common fixed point of two relatively nonexpansive mappings in a banach space and an element of the set of solutions of an equilibrium problem in a banach space respectively our results are applicable to a wide class of mappings

strong convergence theorems of total quasi φ asymptotically nonexpansive semi groups in banach spaces the purpose of this article is first to introduce the concept of total quasi f asymptotically nonexpansive semigroups which contains many kinds of semi groups as its special cases and then to modify the halpern mann type iteration algorithm for this kind of semi groups to have the strong convergence under a limit condition only in the framework of banach spaces the results presented in the paper improve and extend the corresponding recent results announced by many authors

strong convergence theorem for pseudo contractive mappings in hilbert spaces abstract the purpose of this paper is to construct an ishikawa type of hybrid algorithm for pseudo contractive mappings in hilbert spaces our results extend the recent ones announced by yao et al y h yao y c liou g marino a hybrid algorithm for pseudo contractive mappings nonlinear anal 71 2009 4997 5002 and many others

a hybrid scheme for finite families of equilibrium variational inequality and fixed point problems we introduce an iterative process for finding an element in the common fixed point set of finite family of closed relatively quasi nonexpansive mappings common solutions of finite family of equilibrium problems and common solutions of finite family of variational inequality problems for monotone mappings in banach spaces our theorem extends and unifies most of the results that have been proved for this important class of nonlinear operators

strong convergence theorem by a new hybrid method for equilibrium problems and variational inequality problems abstract in this paper we prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of the solutions of the variational inequality problem by using a new hybrid method we obtain a new result for finding a solution of an equilibrium problem and the solutions of the variational inequality problem

asymptotically strict pseudocontractive mappings in the intermediate sense abstract it is proved that the modified mann iteration process x n 1 1 n x n n t n x n n n where n is a sequence in 0 1 with n 1 for some 0 1 converges weakly to a fixed point of an asymptotically strict pseudocontractive mapping t in the intermediate sense which is not necessarily lipschitzian we also develop cq method for this modified mann iteration process which generates a strongly convergent sequence