Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces

Chin-Tzong Pang and Eskandar Naraghirad

Abstract and Applied Analysis, 2013, vol. 2013, 1-14

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.

Date: 2013
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:316813

DOI: 10.1155/2013/316813

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