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Abstract and Applied Analysis
Volume 2013, Article ID 316813, 14 pages
http://dx.doi.org/10.1155/2013/316813
Research Article

Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces

1Department of Information Management, Yuan Ze University, Chung-Li 32003, Taiwan
2Department of Mathematics, Yasouj University, Yasouj 75918, Iran
3Department of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, Taiwan

Received 20 September 2013; Accepted 11 November 2013

Academic Editor: Chi-Ming Chen

Copyright © 2013 Chin-Tzong Pang and Eskandar Naraghirad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We first introduce a new class of mappings called Bregman asymptotic pointwise nonexpansive mappings and investigate the existence and the approximation of fixed points of such mappings defined on a nonempty, bounded, closed, and convex subset C of a real Banach space E. Without using the original Opial property of a Banach space E, we prove weak convergence theorems for the sequences produced by generalized Mann and Ishikawa iteration processes for Bregman asymptotic pointwise nonexpansive mappings in a reflexive Banach space E. Our results are applicable in the function spaces , where is a real number.