Strong convergence of approximants to fixed points of Lipschitzian pseudocontractive maps

H. Zegeye, E. Prempeh

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

Let E be a real q-uniformly smooth Banach space which is also uniformly convex (for example, Lp or lp spaces, 1 < p < ∞) and K be a nonempty closed convex and bounded subset of E with φ ≠ int (K). Let T: K → K be a Lipschitzian pseudocontractive mapping such that for z ∈ int (K), ∥z - Tz∥ < ∥x - Tx∥, for all x ∈ ∂(K). Then for z0 ∈ K arbitrary, the iteration process (zn) defined by zn+1: = (1 - μn+1)z+μn+1yn; yn: = (1 - αn)zn + αnTzn converges strongly to a fixed point of T, provided that (μn) and (αn) satisfy certain conditions. Moreover, if T is strictly pseudocontractive with a nonempty fixed-point set, then it is proved that the Mann type iteration scheme converges strongly to a fixed point of T.

Original languageEnglish
Pages (from-to)339-346
Number of pages8
JournalComputers and Mathematics with Applications
Volume44
Issue number3-4
DOIs
Publication statusPublished - Jan 1 2002

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Banach spaces
Strong Convergence
Fixed point
Q-uniformly Smooth Banach Spaces
Lipschitzian Mapping
Converge
Pseudocontractive Mapping
Uniformly Convex
Fixed Point Set
Iteration Scheme
Lp Spaces
Strictly
Iteration
Closed
Subset
Arbitrary

All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics

Cite this

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Strong convergence of approximants to fixed points of Lipschitzian pseudocontractive maps. / Zegeye, H.; Prempeh, E.

In: Computers and Mathematics with Applications, Vol. 44, No. 3-4, 01.01.2002, p. 339-346.

Research output: Contribution to journalArticle

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