Strong convergence of the modified Ishikawa iterative method for infinitely many nonexpansive mappings in Banach spaces

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Author list: Katchang P., Kumam P.

Publisher: Elsevier

Publication year: 2010

Journal: Computers & Mathematics with Applications (0898-1221)

Volume number: 59

Issue number: 4

Start page: 1473

End page: 1483

Number of pages: 11

ISSN: 0898-1221

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-75549089411&doi=10.1016%2fj.camwa.2010.01.025&partnerID=40&md5=9e21848bf5b3ce1a7aba0c28ec8c01c7

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we introduce a new modified Ishikawa iterative process for computing fixed points of an infinite family nonexpansive mapping in the framework of Banach spaces. Then, we establish the strong convergence theorem of the proposed iterative scheme under some mild conditions which solves a variational inequality. The results obtained in this paper extend and improve on the recent results of Qin et al. [Strong convergence theorems for an infinite family of nonexpansive mappings in Banach spaces, Journal of Computational and Applied Mathematics 230 (1) (2009) 121-127], Cho et al. [Approximation of common fixed points of an infinite family of nonexpansive mappings in Banach spaces, Computers and Mathematics with Applications 56 (2008) 2058-2064] and many others. ฉ 2010 Elsevier Ltd. All rights reserved.

Keywords

Infinite family