Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings

H. Zegeye, N. Shahzad

Research output: Contribution to journalArticle

48 Citations (Scopus)

Abstract

Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let Ti:C→H,i=1,2,...,N, be a finite family of generalized asymptotically nonexpansive mappings. It is our purpose, in this paper to prove strong convergence of Mann's type method to a common fixed point of Ti:i=1,2,...,N provided that the interior of common fixed points is nonempty. No compactness assumption is imposed either on T or on C. As a consequence, it is proved that Mann's method converges for a fixed point of nonexpansive mapping provided that interior of F(T)≠Combining long solidus overlay. The results obtained in this paper improve most of the results that have been proved for this class of nonlinear mappings.

Original languageEnglish
Pages (from-to)4007-4014
Number of pages8
JournalComputers and Mathematics with Applications
Volume62
Issue number11
DOIs
Publication statusPublished - Dec 1 2011

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Asymptotically Nonexpansive Mapping
Iteration Method
Common Fixed Point
Interior
Nonlinear Mapping
Nonexpansive Mapping
Overlay
Strong Convergence
Compactness
Hilbert space
Fixed point
Hilbert spaces
Set theory
Converge
Closed
Subset
Family
Class

All Science Journal Classification (ASJC) codes

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

Cite this

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Convergence of Mann's type iteration method for generalized asymptotically nonexpansive mappings. / Zegeye, H.; Shahzad, N.

In: Computers and Mathematics with Applications, Vol. 62, No. 11, 01.12.2011, p. 4007-4014.

Research output: Contribution to journalArticle

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