Iterative algorithm for multi-valued pseudocontractive mappings in Banach spaces

Eric U. Ofoedu, Habtu Zegeye

Research output: Contribution to journalArticle

11 Citations (Scopus)

Abstract

Let D be nonempty open convex subset of a real Banach space E. Let T:D→KC(E) be a continuous pseudocontractive mapping satisfying the weakly inward condition and let u∈D be fixed. Then for each t∈(0,1) there exists yt∈D satisfying yt∈tTyt+(1-t)u. If, in addition, E is reflexive and has a uniformly Gâteaux differentiable norm, and is such that every closed convex bounded subset of D has fixed point property for nonexpansive self-mappings, then T has a fixed point if and only if {yt} remains bounded as t→1; in this case, {yt} converges strongly to a fixed point of T as t→1-. Moreover, an explicit iteration process which converges strongly to a fixed point of T is constructed in the case that T is also Lipschitzian.

Original languageEnglish
Pages (from-to)68-76
Number of pages9
JournalJournal of Mathematical Analysis and Applications
Volume372
Issue number1
DOIs
Publication statusPublished - Dec 1 2010

Fingerprint

Pseudocontractive Mapping
Multivalued Mapping
Banach spaces
Iterative Algorithm
Fixed point
Banach space
Set theory
Converge
Fixed Point Property
Subset
Differentiable
If and only if
Iteration
Norm
Closed

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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Iterative algorithm for multi-valued pseudocontractive mappings in Banach spaces. / Ofoedu, Eric U.; Zegeye, Habtu.

In: Journal of Mathematical Analysis and Applications, Vol. 372, No. 1, 01.12.2010, p. 68-76.

Research output: Contribution to journalArticle

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