[PDF] Top 20 New Iterative Approximation Methods for a Countable Family of Nonexpansive Mappings in Banach Spaces

... finite family of nonexpansive mappings has been considered by many authors see 1–4 and the references ...a family of nonexpansive mappings see 5, ...a family of ... See full document

... We first prove the existence of a solution of the generalized equilibrium problem (GEP) using the KKM mapping in a Banach space setting. Then, by virtue of this result, we construct a hybrid algorithm for finding ... See full document

... a countable family of relatively nonexpansive mappings and the set of solutions of an equilibrium problem in the framework of Banach ... See full document

... an iterative method to construct the Bregman projection of a point onto a countable intersection of closed and convex sets in reflexive Banach ...a Banach space, in , Alber [] first ... See full document

... Let K be a nonempty closed convex subset of a uniformly convex Banach space E. Let S : K→K be a nonexpansive mapping and let T : K→K be an asymptotically nonexpansive mapping. In 10, the authors ... See full document

... general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach ...relatively nonexpansive mapping and the ... See full document

... general iterative scheme for finding a common element of the set of equilibrium problems and fixed point problems of a countable family of nonexpansive mappings in Hilbert ... See full document

... real Banach space, C a nonempty closed convex subset of a Banach space X and let P : X → C be the nonexpansive retraction of X onto C, T : C → X a given ...be nonexpansive if kT x − T yk ≤ kx ... See full document

... a new hybrid iteration method for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces, and then we discuss the strong ... See full document

... a new iterative scheme and to get a strong convergence theorem for a countable family of relatively quasi-nonexpansive mappings and a system of equilibrium problems in a ... See full document

... In order to prove the main results of this paper, we need the following lemmas. Lemma 1.2 [2]. Let E be a uniformly convex Banach space, let K be a nonempty closed convex subset of E, and let T : K → K be a ... See full document

... a Banach space and Shioji and Takahashi [19] im- proved Wittmann’s result to a certain Banach ...above iterative scheme with the necessary conditions on the parameters and some additional conditions ... See full document

... finite family of relatively nonexpansive mappings in Banach ...convex Banach space E, then the generalized projection Π C (see, Alber [15] or Kamimura and ... See full document

... a Banach space ...hybrid iterative scheme for finding a common element of the set of solutions of MEP(f, ϕ , C) and the set of common fixed points of a countable family of quasi- φ ... See full document

... onto C is not generally nonexpansive. Our purpose in the present paper is to obtain an analogous result for a finite family of relatively nonexpansive mappings in Banach spaces. ... See full document

... of iterative algorithms for nonexpansive mappings, nonexpansive semigroup, and pseudocontractive semigroup in Banach spaces see, ...a nonexpansive mapping, and A be a ... See full document

... 12 I. Yamada, “The hybrid steepest descent method for the variational inequality problem over the intersection of fixed point sets of nonexpansive mappings,” in Inherently Parallel Algorithms in Feasibility ... See full document

... limit is a solution of certain variational inequality. Next, we study the viscosity approximation with the weakly contractive mapping to a fixed point of nonexpansive mapping in the same Banach ... See full document

... for all x ∈ E. It is known that E is smooth if and only if the duality mapping J is single valued, and that if E has a uniformly Gâteaux differentiable norm, J is uniformly norm-to- weak ∗ continuous on each bounded ... See full document

... finite family of ...generalized nonexpansive mappings and present the analogue version of the result above for Ibaraki-Takahashi’s generalized nonexpansive ...relatively nonexpansive ... See full document