A new hybrid algorithm for a system of equilibrium problems and variational inclusion

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Publication Details

Author list: Jitpeera T., Kumam P.

Publisher: Springer

Publication year: 2011

Journal: Annali dell'Universita di Ferrara (0430-3202)

Volume number: 57

Issue number: 1

Start page: 89

End page: 108

Number of pages: 20

ISSN: 0430-3202

eISSN: 1827-1510

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-79958175118&doi=10.1007%2fs11565-010-0110-4&partnerID=40&md5=e1e465700722196cf714975b728ae05c

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this paper is to consider a shrinking projection method of finding the common element of the set of common fixed points for a finite family of a ξ-strict pseudo-contraction, the set of solutions of a systems of equilibrium problems and the set of solutions of variational inclusions. Then, we prove strong convergence theorems of the iterative sequence generated by the shrinking projection method under some suitable conditions in a real Hilbert space. Our results improve and extend recent results announced by Peng, Wang, Shyu and Yao (J Inequal Appl, 2008:15, Article ID 720371, 2008), Takahashi, Takeuchi and Kubota (J Math Anal Appl 341:276-286, 2008), Takahashi and Takahashi (Nonlinear Anal 69:1025-1033, 2008) and many others. © 2010 Università degli Studi di Ferrara.

Keywords

Generalized mixed equilibrium problem, Inverse-strongly monotone mapping