Iterative methods for fixed points of asymptotically weakly contractive maps

Robert Gilbert, C. E. Chidume, H. Zegeye, S. J. Aneke

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Suppose K is a closed convex nonexpansive retract of a real uniformly smooth Banach space E with P as the nonexpansive retraction. Suppose T : K → E is an asymptotically d-weakly contractive map with sequence {k n }, k n ≥ 1, lim k n = 1 and with F(T) n int (K) ≠ øF(T):= {x ∈ K: Tx = x}. Suppose {x n } is iteratively defined by x n+1 = P((l − k n α n )x n +k n α n T(PT) n−l x n ), n = 1,2,.., x 1 ∈ K, where α n ∈ (0, l) satisfies lim α n = 0 and Σα n = ∞. It is proved that {x n } converges strongly to some x * ∈ F(T)∩ int K. Furthermore, if K is a closed convex subset of an arbitrary real Banach space and T is, in addition uniformly continuous, with F(T) ≠ ø, it is proved that {x n } converges strongly to some x * ∈ F(T). The author undertook this work when he was visiting the Abdus Salam International Center for Theoretical Physics, Trieste, Italy, as a postdoctoral fellow. Department of Mathematics, University of Nigeria, Nsukka.

Original languageEnglish
Pages (from-to)701-712
Number of pages12
JournalApplicable Analysis
Volume82
Issue number7
DOIs
Publication statusPublished - Jul 2003

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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