Weak and strong convergence theorems of implicit iteration process on Banach spaces

Strong Convergence of Non-Implicit Iteration Process with Errors in Banach Spaces

and Applied Analysis 3 Lemma 1.1 see 21 . let X be a uniformly convex Banach space. Let b and c be two constants with 0 < b < c < 1. Suppose that {tn} is a sequence in b, c . Let {xn} and {yn} be two sequences in X such that lim sup n→∞ ‖xn‖ ≤ d, lim sup n→∞ ∥ yn ∥ ∥ ≤ d, lim n→∞ ∥ tnxn 1 − tn yn ∥ ∥ d 1.8 hold for some d ≥ 0, then limn→∞‖xn − yn‖ 0. Lemma 1.2 see 26 . Let {an}, {bn}, and {cn} ...

Strong Convergence of an Implicit Iteration Process for Two Asymptotically Nonexpansive Mappings in Banach Spaces

The purpose of this paper is to introduce an implicit iteration process for approximating common fixed points of two asymptotically nonexpansive mappings and to prove strong convergence theorems in uniformly convex Banach spaces.

Convergence of an Implicit Iteration for Affine Mappings in Normed and Banach Spaces

Weak and Strong Convergence of an Implicit Iteration Process for an Asymptotically Quasi-I-Nonexpansive Mapping in Banach Space

We prove the weak and strong convergence of the implicit iterative process to a common fixed point of an asymptotically quasi-I-nonexpansive mapping T and an asymptotically quasi-nonexpansive mapping I, defined on a nonempty closed convex subset of a 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.