A new modified block iterative algorithm for uniformly quasi-φ- asymptotically nonexpansive mappings and a system of generalized mixed equilibrium problems

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Author list: Saewan S., Kumam P.

Publisher: SpringerOpen

Publication year: 2011

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

Volume number: 2011

ISSN: 1687-1820

eISSN: 1687-1812

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84866057449&doi=10.1186%2f1687-1812-2011-35&partnerID=40&md5=8f355056be9a09175f6992267f3d05d0

Languages: English-Great Britain (EN-GB)

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Abstract

In this paper, we introduce a new modified block iterative algorithm for finding a common element of the set of common fixed points of an infinite family of closed and uniformly quasi-φ-asymptotically nonexpansive mappings, the set of the variational inequality for an α-inverse-strongly monotone operator, and the set of solutions of a system of generalized mixed equilibrium problems. We obtain a strong convergence theorem for the sequences generated by this process in a 2-uniformly convex and uniformly smooth Banach space. Our results extend and improve ones from several earlier works. © 2011 Saewan and Kumam; licensee Springer.

Keywords

A system of generalized mixed equilibrium problem