Approximation methods for solving equilibrium problems and variational inequality problems of an infite family of nonexpansive mappings

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Publication Details

Author listRattana P., Tanutpanit T., Kumam P.

PublisherHikari

Publication year2010

JournalInternational Journal of Mathematical Analysis (1312-8876)

Volume number4

Issue number41-44

Start page2121

End page2141

Number of pages21

ISSN1312-8876

URLhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-78650424394&partnerID=40&md5=e72f0a6709f7d8540888fe1c01cc8df4

LanguagesEnglish-Great Britain (EN-GB)


Abstract

In this paper, we introduce an iterative scheme by a modified hybrid extragradient method for finding a common element of the set of fixed points of a countable family of nonexpansive mappings, the set of solutions of an equilibrium problem and the set of solutions of the variational inequality for α-inverse-strongly monotone mappings in a real Hilbert space. We show that the iterative sequence converges strongly to a common element of the above three sets, which solves some fixed point problems, variational inequality problems and equilibrium problems by using the hybrid method in mathematical programming which are connected with optimization problems. The results extend and improve the recent result of Kumam [11], Shinzato and Takahashi [21], Tada and Takahashi [24] and Takahashi et. al. [27].


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Last updated on 2022-06-01 at 15:39