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

Naseer Shahzad, Habtu Zegeye

Research output: Contribution to journalArticle

118 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

Fingerprint

Ishikawa Iteration
Mann Iteration
Multivalued Map
Multivalued Mapping
Iteration Scheme
Banach spaces
Iterative Process
Banach space
Nonexpansive Map
Strong Theorems
Strong Convergence
Convergence Theorem

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

Cite this

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On Mann and Ishikawa iteration schemes for multi-valued maps in Banach spaces. / Shahzad, Naseer; Zegeye, Habtu.

In: Nonlinear Analysis, Theory, Methods and Applications, Vol. 71, No. 3-4, 01.08.2009, p. 838-844.

Research output: Contribution to journalArticle

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