Implicit Mann approximation with perturbations for nonexpansive semigroups in CAT(0) spaces

Xue Song Li, Tsz Leung Yip

Research output: Journal article publicationJournal articleAcademic researchpeer-review

Abstract

In this paper, we study the convergence of implicit Mann iteration processes with bounded perturbations for approximating a common fixed point of nonexpansive semigroup in CAT(0) spaces. We obtain the Δ-convergence results of implicit Mann iteration schemes with bounded perturbations for a family of nonexpansive mappings in CAT(0) spaces. Under certain and different conditions, we also get the strong convergence theorems of implicit Mann iteration schemes with bounded perturbations for nonexpansive semigroups in CAT(0) spaces. The results presented in this paper extend and enrich the existing literature.
Original languageEnglish
Article number145
JournalFixed Point Theory and Applications
Volume2012
DOIs
Publication statusPublished - 1 Jan 2012

Keywords

  • CAT(0) space
  • Common fixed point
  • Implicit approximation
  • Nonexpansive semigroup
  • Δ-convergence

ASJC Scopus subject areas

  • Geometry and Topology
  • Applied Mathematics

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