[PDF] Top 20 A strong convergence theorem on solving common solutions for generalized equilibrium problems and fixed-point problems in Banach space

... Throughout this paper, unless other stated, ℝ and J are denoted by the set of the real numbers and the set {1, 2,..., N}, respectively, where N is any given positive integer. Let E be a real Banach space ... See full document

... Theorem . Let C be a nonempty closed convex subset of a Hilbert space H and let F be a bifunction from C × C to R which satisfies (A)-(A). Let T : C → H be a k-strict pseudo-contraction, B : C → H be a β ... See full document

... convex Banach space which also enjoys the Kadec-Klee property, and let C be a nonempty closed and convex subset of ...a generalized asymptotically quasi-φ-nonexpansive ... See full document

... the solutions of problems ...investigate generalized asymptoti- cally quasi-φ-nonexpansive mappings and problem ...A strong convergence theorem for common solutions ... See full document

... If S is the identity, we find the following result on the generalized equilibrium problem. Corollary . Let C be a nonempty closed convex subset of a Hilbert space H and let F be a bifunction from C ... See full document

... a common element of a solution set of a generalized equilibrium problem, of a solution set solutions of a variational inequality problem and of a fixed point set of a strict ... See full document

... of solutions of ...minimization problems. Convex minimization problems have a great impact and influence in the development of almost all branches of pure and applied ...Hilbert space H ... See full document

... It is remarked that the set-valued mapping J is nonempty, closed and convex in a real Banach space whereas J is single-valued in a reflexive, strictly convex and smooth Banach space. ... See full document

... a common element of the set of common solutions of generalized mixed equilibrium problems and the set of common fixed points of an finite family of nonexpansive ... See full document

... Hilbert space, the normal Mann ’ s itera- tive [10] algorithm has only weak convergence, in general, even for nonexpansive map- ...obtain strong convergence, some modifications of the normal ... See full document

... the problems of finding a common element in the set of solution of variational inequalities for an inverse-strongly monotone mapping and in the set of fixed points of nonexpansive mappings or strict ... See full document

... a common element of the set of fixed points of a relatively nonexpansive mapping and the set of solutions of an equilibrium problem in a Banach ...the strong convergence ... See full document

... a strong convergence theorem for finding a common element of the set of solutions for generalized equilibrium problems, the set of fixed points of a ... See full document

... in Theorem . has only weak convergence. In order to obtain strong convergence theorem, very recently, Zeng and Yao [] further introduced a new extragradient method for finding a ... See full document

... a common element of the set of fixed points of an infinite family of nonexpansive mappings, the set of solutions of the generalized equilibrium problem, and the set of solutions ... See full document

... constraint. Solving such problems, we have to obtain some solution which is simultaneously the solution of two or more subproblems or the solution of one subproblem on the solution set of another ... See full document

... a strong convergence theorem by using a hybrid method for finding a common element of the set of solutions for generalized mixed equilibrium problems, the set of ... See full document

... Hilbert space H, A : C → H be an α-inverse-strongly monotone mapping, S : C → C be a quasi-nonexpansive mapping such that I – S is demiclosed at zero, and B be a maximal monotone operator on H such that the domain ... See full document

... In this section, we give an application of Theorem . to the split feasibility problem (say SFP, for short), which was introduced by Censor and Elfving []. Since its inception in , the split feasibility ... See full document

... important problems have reformulations which require finding solutions of equi- libriums ...inverse problems, network alloca- tion, transportation problems and optimization problems; see ... See full document