Strong Convergence of Non-Implicit Iteration Process with Errors in 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 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 of an Implicit Iteration for Affine Mappings in Normed and Banach Spaces

Strong Convergence Theorems of Ishikawa Iteration Process With Errors For Fixed points of Lipschitz Continuous Mappings in Banach Spaces

Let q > 1 and E be a real q-uniformly smooth Banach space, K be a nonempty closed convex subset of E and T : K → K be a Lipschitz continuous mapping. Let {un} and {vn} be bounded sequences in K and {αn} and {βn} be real sequences in [0, 1] satisfying some restrictions. Let {xn} be the sequence generated from an arbitrary x1 ∈ K by the Ishikawa iteration process with errors: yn = (1− βn)xn + βnT...