Minimum-norm fixed point of pseudocontractive mappings

Habtu Zegeye, Naseer Shahzad, Mohammad Ali Alghamdi

Research output: Contribution to journalArticle

12 Citations (Scopus)

Abstract

Let K be a closed convex subset of a real Hilbert space H and let T:K→K be a continuous pseudocontractive mapping. Then for βε(0,1) and each tε(0,1), there exists a sequence { yt}⊂K satisfying yt=βPK[(1-t)yt]+(1-β)T(yt) which converges strongly, as t→0+, to the minimum-norm fixed point of T. Moreover, we provide an explicit iteration process which converges strongly to a minimum-norm fixed point of T provided that T is Lipschitz. Applications are also included. Our theorems improve several results in this direction.

Original languageEnglish
Article number926017
JournalAbstract and Applied Analysis
Volume2012
DOIs
Publication statusPublished - Dec 1 2012

Fingerprint

Pseudocontractive Mapping
Hilbert spaces
Set theory
Fixed point
Converge
Norm
Lipschitz
Hilbert space
Iteration
Closed
Subset
Theorem

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

Zegeye, Habtu ; Shahzad, Naseer ; Alghamdi, Mohammad Ali. / Minimum-norm fixed point of pseudocontractive mappings. In: Abstract and Applied Analysis. 2012 ; Vol. 2012.
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Minimum-norm fixed point of pseudocontractive mappings. / Zegeye, Habtu; Shahzad, Naseer; Alghamdi, Mohammad Ali.

In: Abstract and Applied Analysis, Vol. 2012, 926017, 01.12.2012.

Research output: Contribution to journalArticle

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