Strong convergence theorems for common fixed points of uniformly L-Lipschitzian pseudocontractive semi-groups

C. E. Chidume, H. Zegeye

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let K be a nonempty closed convex subset of a uniformly convex real Banach space E which has uniformly Gâteaux differentiable norm. Let (Formula presented.) be a strongly continuous uniformly L-Lipschitzian semi-group of pseudocontractive mappings from K into E satisfying the weakly inward condition with a nonempty common fixed point set. Then, for a given u∈K, there exists a unique point u n in K satisfying (Formula presented.), where α n ∈[0,1) and t n > 0 are real sequences satisfying appropriate conditions. Furthermore, {u n } converges strongly to a fixed point of (Formula presented.). Moreover, explicit iteration procedures which converge strongly to a fixed point of (Formula presented.) are constructed. A corollary of this result gives an affirmative answer to a recent question posed in Suzuki (2003, Proceedings of the American Mathematical Society, 131, 2133–2136).

Original languageEnglish
Pages (from-to)353-366
Number of pages14
JournalApplicable Analysis
Volume86
Issue number3
DOIs
Publication statusPublished - Mar 2007

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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