Strong convergence theorem for two asymptotically quasi-nonexpansive mappings with errors in Banach space

Convergence theorems of implicit iterates with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces

In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.

Convergence theorems of multi-step iterative algorithm with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces

The purpose of this paper is to study and give the necessary andsufficient condition of strong convergence of the multi-step iterative algorithmwith errors for a finite family of generalized asymptotically quasi-nonexpansivemappings to converge to common fixed points in Banach spaces. Our resultsextend and improve some recent results in the literature (see, e.g. [2, 3, 5, 6, 7, 8,11, 14, 19]).

A Mean Ergodic Theorem For Asymptotically Quasi-Nonexpansive Affine Mappings in Banach Spaces Satisfying Opial's Condition

Strong Convergence Theorem for Two Commutative Asymptotically Nonexpansive Mappings in Hilbert Space

where tn → 1 n → ∞ . We may assume that tn ≥ 1 for all n 1, 2, 3, . . . . Denote by F T the set of fixed points of T . Throughout this paper T and S : C → C are two commutative asymptotically nonexpansive mappings with asymptotical coefficients {tn} and {sn}, respectively. Suppose that F : F T ∩F S / ∅ 1, Goebel and Kirk’s theorem makes it possible . It is well known that F T and F S are convex...

Strong Convergence Theorems for Bregman Quasi–asymptotically Nonexpansive Mappings and Equilibrium Problem in Reflexive Banach Spaces

The purpose of this article is to propose an iteration algorithm for Bergman quasiasymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of reflexive Banach spaces. As applications, we apply our results to a system of equilibrium problems. The results presented in the paper improve and extend the corresponding results of Reich and Sabach...