Viscosity approximation methods for pseudocontractive mappings in Banach spaces

Habtu Zegeye, Naseer Shahzad, Tefera Mekonen

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20 Citations (Scopus)

Abstract

Let K be a closed convex subset of a Banach space E and let T : K → E be a continuous weakly inward pseudocontractive mapping. Then for t ∈ (0, 1), there exists a sequence {yt} ⊂ K satisfying yt = (1 - t)f(yt) + tT(yt), where f ∈ ΠK {colon equals} {f : K → K, a contraction with a suitable contractive constant}. Suppose further that F(T) ≠ ∅ and E is reflexive and strictly convex which has uniformly Gâteaux differentiable norm. Then it is proved that {yt} converges strongly to a fixed point of T which is also a solution of certain variational inequality. Moreover, an explicit iteration process which converges strongly to a fixed point of T and hence to a solution of certain variational inequality is constructed provided that T is Lipschitzian.

Original languageEnglish
Pages (from-to)538-546
Number of pages9
JournalApplied Mathematics and Computation
Volume185
Issue number1
DOIs
Publication statusPublished - Feb 1 2007

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All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

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