Approximation of fixed points of weakly contractive nonself maps in Banach spaces

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

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49 Citations (Scopus)

Abstract

Let K be a closed convex subset of a real uniformly smooth Banach space E. Suppose K is a nonexpansive retract of E with P as the nonexpansive retraction. Let T : K → E be a d-weakly contractive map such that a fixed point x* ∈ int(K) of T exists. It is proved that a descent-like approximation sequence converges strongly to x*. Furthermore, if K is a nonempty closed convex subset of an arbitrary real Banach space and T:K → K is a uniformly continuous d-weakly contractive map with F(T) := (x ∈ K: Tx = x) ≠ Ø, it is proved that a descent-like approximation sequence converges strongly to x* ∈ F(T).

Original languageEnglish
Pages (from-to)189-199
Number of pages11
JournalJournal of Mathematical Analysis and Applications
Volume270
Issue number1
DOIs
Publication statusPublished - Jun 1 2002

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All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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