Abstract and Applied Analysis

Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces

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 ${L}^{p}$, where $1 is a real number.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 316813, 14 pages.

Dates
First available in Project Euclid: 26 February 2014

https://projecteuclid.org/euclid.aaa/1393442126

Digital Object Identifier
doi:10.1155/2013/316813

Mathematical Reviews number (MathSciNet)
MR3147820

Zentralblatt MATH identifier
1320.47052

Citation

Pang, Chin-Tzong; Naraghirad, Eskandar. Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 316813, 14 pages. doi:10.1155/2013/316813. https://projecteuclid.org/euclid.aaa/1393442126

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