A viscosity extragradient method for an equilibrium problem and fixed point problem in Hilbert space

Journal article

Authors/Editors

POOM KUMAM

Strategic Research Themes

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Publication Details

Author list: Wang S., Zhao M., Kumam P., Cho Y.J.

Publisher: Springer

Publication year: 2018

Journal: Journal of Fixed Point Theory and Applications (1661-7738)

Volume number: 20

Issue number: 1

ISSN: 1661-7738

eISSN: 1661-7746

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-85041541723&doi=10.1007%2fs11784-018-0512-y&partnerID=40&md5=663ba6a8f271341333787e91cdb2a0d3

Languages: English-Great Britain (EN-GB)

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Abstract

In the literature, few viscosity extragradient methods are used to solve the pseudomonotone and Lipschitz-type continuous equilibrium problems so far. In this paper, we construct a viscosity extragradient algorithm to find a common element of solution set of a pseudomonotone equilibrium problem and fixed point set of a nonexpansive mapping in Hilbert space and prove the strong convergence for the given algorithm. Finally, some numerical examples are given to illustrate the results of this paper. ฉ 2018, Springer International Publishing AG, part of Springer Nature.

Keywords

Pseudomonotone equilibrium problem