On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces

Naseer Shahzad, Habtu Zegeye

Research output: Contribution to journalArticle

134 Citations (Scopus)

Abstract

We prove strong convergence theorems for the Ishikawa iteration scheme involving quasi-nonexpansive multi-valued maps. We also construct an iteration scheme which removes a restrictive condition in Song and Wang results [Y. Song, H. Wang, Erratum to "Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces" [Comput. Math. Appl. 54 (2007) 872-877], Comput. Math. Appl. 55 (2008) 2999-3002]. Our results provide an affirmative answer to Panyanak's question [Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comput. Math. Appl., 54 (2007), 872-877], in a more general setting.

Original languageEnglish
Pages (from-to)838-844
Number of pages7
JournalNonlinear Analysis, Theory, Methods and Applications
Volume71
Issue number3-4
DOIs
Publication statusPublished - Aug 1 2009

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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