Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces | Zendy

Chin-Tzong Pang | Zendy; Eskandar Naraghirad | Zendy

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Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces

Author(s) -

Chin-Tzong Pang,

Eskandar Naraghirad

Publication year - 2013

Publication title -

abstract and applied analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.228

H-Index - 56

eISSN - 1687-0409

pISSN - 1085-3375

DOI - 10.1155/2013/316813

Subject(s) - pointwise , mathematics , banach space , bounded function , regular polygon , pure mathematics , pointwise convergence , discrete mathematics , combinatorics , mathematical analysis , geometry , approx , computer science , operating system

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 mappingsin a reflexive Banach space E. Our results are applicable in the function spaces Lp, where 1

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