Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces

Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces

Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X . Let T : C→ C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point...

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

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.

Fixed point solutions of variational inequalities for a semigroup of asymptotically nonexpansive mappings in Banach spaces

The purpose of this article is to introduce two iterative algorithms for finding a common fixed point of a semigroup of asymptotically nonexpansive mappings which is a unique solution of some variational inequality. We provide two algorithms, one implicit and another explicit, from which strong convergence theorems are obtained in a uniformly convex Banach space, which admits a weakly continuou...

Fixed Point Theorems for a Semigroup of Total Asymptotically Nonexpansive Mappings in Uniformly Convex Banach Spaces

In this paper, we provide existence and convergence theorems of common fixed points for left (or right) reversible semitopological semigroups of total asymptotically nonexpansive mappings in uniformly convex Banach spaces. The results presented in this paper extend and improve some recent results announced by other authors.