Convergence of Ishikawa's iteration method for pseudocontractive mappings

Habtu Zegeye, Naseer Shahzad, Mohammad A. Alghamdi

Research output: Contribution to journalArticle

23 Citations (Scopus)

Abstract

Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→C,i=1,2,⋯,N, be a finite family of Lipschitz pseudocontractive mappings. It is our purpose, in this paper, to prove strong convergence of Ishikawa's method to a common fixed point of a finite family of Lipschitz pseudocontractive mappings provided that the interior of the common fixed points is nonempty. No compactness assumption is imposed either on T or on C. Moreover, computation of the closed convex set Cn for each n<1 is not required. The results obtained in this paper improve on most of the results that have been proved for this class of nonlinear mappings.

Original languageEnglish
Pages (from-to)7304-7311
Number of pages8
JournalNonlinear Analysis, Theory, Methods and Applications
Volume74
Issue number18
DOIs
Publication statusPublished - Dec 1 2011

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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