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Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces

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  • Chin-Tzong Pang
  • Eskandar Naraghirad

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.

Suggested Citation

  • Chin-Tzong Pang & Eskandar Naraghirad, 2013. "Bregman Asymptotic Pointwise Nonexpansive Mappings in Banach Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-14, December.
    • Handle: RePEc:hin:jnlaaa:316813
    DOI: 10.1155/2013/316813
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