Convergence theorems for fixed points of demicontinuous pseudocontractive mappings

C. E. Chidume, H. Zegeye

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3 Citations (Scopus)

Abstract

Let D be an open subset of a real uniformly smooth Banach space E. Suppose T: D̄ → E is a demicontinuous pseudocontractive mapping satisfying an appropriate condition, where D̄ denotes the closure of D. Then, it is proved that (i) D̄ ⊆ ℛ (I + r (I-T)) for every r > 0; (ii) for a given y0 ∈ D, there exists a unique path t → yt ∈ D̄, t ∈ [0, 1], satisfying yt := tTyt + (1-t) y0. Moreover, if F (T) ≠ ∅ or there exists y0 ∈ D such that the set K := {y ∈ D: T y = λ y + (1-λ) y0 for λ >1} is bounded, then it is proved that, as t → 1-, the path {yt} converges strongly to a fixed point of T. Furthermore, explicit iteration procedures with bounded error terms are proved to converge strongly to a fixed point of T.

Original languageEnglish
Pages (from-to)67-77
Number of pages11
JournalFixed Point Theory and Applications
Volume2005
Issue number1
DOIs
Publication statusPublished - Dec 1 2005

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All Science Journal Classification (ASJC) codes

  • Geometry and Topology
  • Applied Mathematics

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