Strong convergence theorems for Bregman totally quasi-asymptotically nonexpansive mappings in reflexive Banach spaces

S. S. Chang, L. Wang, X. R. Wang, Chi Kin Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

11 Citations (Scopus)

Abstract

The purpose of this article is by using the shrinking projection method introduced by Takahashi, Kubota and Takeuchi to propose an iteration algorithm for Bregman total quasi-asymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of reflexive Banach spaces. As applications, we apply our results to a system of equilibrium problems and zero point problem of maximal monotone mappings in reflexive Banach spaces. The results presented in the paper improve and extend the corresponding results of Reich and Sabach (2010) [12], Suantai et al. (2012) [13], Nilsrakoo and Saejung (2011) [11], Qin et al. (2009) [5], Wang et al. (2011) [6], Su et al. (2010) [7], Martinez-Yanes and Xu (2006) [3] and others.
Original languageEnglish
Pages (from-to)38-48
Number of pages11
JournalApplied Mathematics and Computation
Volume228
DOIs
Publication statusPublished - 1 Feb 2014

Keywords

  • Bregman projection
  • Bregman quasi-asymptotically nonexpansive mapping
  • Bregman quasi-nonexpansive mapping
  • Bregman strongly nonexpansive mapping
  • Bregman total quasi-asymptotically nonexpansive mapping
  • Legendre function
  • Totally convex function

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

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