Viscosity approximation methods for pseudocontractive mappings in Banach spaces

Habtu Zegeye, Naseer Shahzad, Tefera Mekonen

Research output: Contribution to journalArticle

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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Viscosity Approximation Method
Pseudocontractive Mapping
Banach spaces
Variational Inequalities
Fixed point
Banach space
Viscosity
Converge
Strictly Convex
Set theory
Differentiable
Contraction
Iteration
Norm
Closed
Subset

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Applied Mathematics

Cite this

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Viscosity approximation methods for pseudocontractive mappings in Banach spaces. / Zegeye, Habtu; Shahzad, Naseer; Mekonen, Tefera.

In: Applied Mathematics and Computation, Vol. 185, No. 1, 01.02.2007, p. 538-546.

Research output: Contribution to journalArticle

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