On the convergence of implicit iteration process with error for a finite family of asymptotically nonexpansive mappings

S. S. Chang, K. K. Tan, Heung Wing Joseph Lee, Chi Kin Chan

Research output: Journal article publicationJournal articleAcademic researchpeer-review

60 Citations (Scopus)

Abstract

The purpose of this paper is to study the weak and strong convergence of implicit iteration process with errors to a common fixed point for a finite family of asymptotically nonexpansive mappings and nonexpansive mappings in Banach spaces. The results presented in this paper extend and improve the corresponding results of [H. Bauschke, The approximation of fixed points of compositions of nonexpansive mappings in Hilbert space, J. Math. Anal. Appl. 202 (1996) 150-159; B. Halpern, Fixed points of nonexpansive maps, Bull. Amer. Math. Soc. 73 (1967) 957-961; P.L. Lions, Approximation de points fixes de contractions, C. R. Acad. Sci. Paris, Ser. A 284 (1977), 1357-1359; S. Reich, Strong convergence theorems for resolvents of accretive operators in Banach spaces, J. Math. Anal. Appl. 75 (1980) 287-292; Z.H. Sun, Strong convergence of an implicit iteration process for a finite family of asymptotically quasi-nonexpansive mappings, J. Math. Anal. Appl. 286 (2003) 351-358; R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491; H.K. Xu, M.G. Ori, An implicit iterative process for nonexpansive mappings, Numer. Funct. Anal. Optimiz. 22 (2001) 767-773; Y.Y. Zhou, S.S. Chang, Convergence of implicit iterative process for a finite family of asymptotically nonexpansive mappings in Banach spaces, Numer. Funct. Anal. Optimiz. 23 (2002) 911-921].
Original languageEnglish
Pages (from-to)273-283
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume313
Issue number1
DOIs
Publication statusPublished - 1 Jan 2006

Keywords

  • Asymptotically nonexpansive mapping
  • Common fixed point
  • Demi-closed principle
  • Implicit iterative sequence with errors for a finite family
  • Nonexpansive mapping
  • Opial condition
  • Semi-compactness

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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