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

H. Zegeye, N. Shahzad

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52 Citations (Scopus)


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
Issue number11
Publication statusPublished - Dec 1 2011


All Science Journal Classification (ASJC) codes

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

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