Multiple-set split feasibility problems for total asymptotically strict pseudocontractions mappings

Li Yang,Shih-Sen Chang,Yeol Je Cho,Jong Kyu Kim

doi:10.1186/1687-1812-2011-77

Abstract

AbstractThe purpose of this article is to propose and investigate an algorithm for solving the multiple-set split feasibility problems for total asymptotically strict pseu-docontractions mappings in infinite-dimensional Hilbert spaces. The results presented in this article improve and extend some recent results of A. Moudafi, H. K. Xu, Y. Censor, A. Segal, T. Elfving, N. Kopf, T. Bortfeld, X. A. Motova, Q. Yang, A. Gibali, S. Reich and others.2000 AMS Subject Classification: 47J05; 47H09; 49J25.

Highlights

Introduction and preliminariesThroughout this article, we always assume that H1, H2 are real Hilbert spaces, “®”, “⇀” are denoted by strong and weak convergence, respectively, and F(T) is the fixed point set of a mapping T.Let G be a nonempty closed convex subset of H1 and T : G ® G a mapping
Banach contraction principle guarantees that every contractive mapping defined on complete metric spaces has a unique fixed point
We remark that the class of weak contractions was introduced by Alber and Guerre-Delabriere [1]

Summary

Introduction

Introduction and preliminariesThroughout this article, we always assume that H1, H2 are real Hilbert spaces, “®”, “⇀” are denoted by strong and weak convergence, respectively, and F(T) is the fixed point set of a mapping T.Let G be a nonempty closed convex subset of H1 and T : G ® G a mapping. They proved that if G is a nonempty closed convex bounded subset of a real uniformly convex Banach space and T is an asymptotically nonexpansive mapping on G, T has a fixed point.

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