Strong convergence theorems for a semigroup of asymptotically nonexpansive mappings

H. Zegeye, N. Shahzad, O. A. Daman

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4 Citations (Scopus)

Abstract

Let K be a nonempty closed convex subset of a real Banach space E. Let T:={T(t):t≥0} be a strongly continuous semigroup of asymptotically nonexpansive mappings from K into K with a sequence {Lt}∪[1,∞). Suppose F(T)≠Ø. Then, for a given uεK there exists a sequence {un}∪K such that un=(1-αn)1tn∫0tnT(s)unds+αnu, for nεN, where tnεR+, {αn}∪(0,1) and {Lt} satisfy certain conditions. Suppose, in addition, that E is reflexive strictly convex with a Gâteaux differentiable norm. Then, the sequence {un} converges strongly to a point of F(T). Furthermore, an explicit sequence {xn} which converges strongly to a fixed point of T is proved.

Original languageEnglish
Pages (from-to)2077-2086
Number of pages10
JournalMathematical and Computer Modelling
Volume54
Issue number9-10
DOIs
Publication statusPublished - Nov 1 2011

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All Science Journal Classification (ASJC) codes

  • Modelling and Simulation
  • Computer Science Applications

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