A hybrid extragradient viscosity approximation method for solving equilibrium problems and fixed point problems of infinitely many nonexpansive mappings

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Jaiboon C., Kumam P.

Publisher: SpringerOpen

Publication year: 2009

Journal: Fixed Point Theory and Applications (1687-1820)

Volume number: 2009

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-69249216652&doi=10.1155%2f2009%2f374815&partnerID=40&md5=f99e6bd2b62d830c21a52e0779bf7bf4

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce a new hybrid extragradient viscosity approximation method for finding the common element of the set of equilibrium problems, the set of solutions of fixed points of an infinitely many nonexpansive mappings, and the set of solutions of the variational inequality problems for β-inverse-strongly monotone mapping in Hilbert spaces. Then, we prove the strong convergence of the proposed iterative scheme to the unique solution of variational inequality, which is the optimality condition for a minimization problem. Results obtained in this paper improve the previously known results in this area.

Keywords