An iterative algorithm for common fixed points for nonexpansive semigroups and strictly pseudo-contractive mappings with optimization problems

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Publication Details

Author list: Katchang P., Kumam P.

Publisher: Springer

Publication year: 2013

Volume number: 56

Issue number: 4

Start page: 1563

End page: 1589

Number of pages: 27

ISSN: 0925-5001

eISSN: 1573-2916

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84880809053&doi=10.1007%2fs10898-012-9927-y&partnerID=40&md5=fc8b1c3e59a2d3b1ebaf28b9345f1732

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a variational inclusion problems for inverse strongly monotone mappings, the set of common fixed points for nonexpansive semigroups and the set of common fixed points for an infinite family of strictly pseudo-contractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (Appl Math Comput 216:51-60, 2010), Hao (Appl Math Comput 217(7):3000-3010, 2010), Jaiboon and Kumam (Nonlinear Anal 73:1180-1202, 2010) and many others. ฉ 2012 Springer Science+Business Media, LLC.

Keywords

Infinite family of strictly pseudo-contractive mappings, Metric projection, Optimization problems, System of mixed equilibrium problem, η-strongly convex functions