A modified mann iterative scheme by generalized f-projection for a countable family of relatively quasi-nonexpansive mappings and a system of generalized mixed equilibrium problems

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

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-s2.0-84877827039&doi=10.1186%2f1687-1812-2011-104&partnerID=40&md5=e5e5071550c8ea63a45313768bf9b9d2

Languages: English-Great Britain (EN-GB)

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Abstract

The purpose of this paper is to introduce a new hybrid projection method based on modified Mann iterative scheme by the generalized f-projection operator for a countable family of relatively quasi-nonexpansive mappings and the solutions of the system of generalized mixed equilibrium problems. Furthermore, we prove the strong convergence theorem for a countable family of relatively quasi-nonexpansive mappings in a uniformly convex and uniform smooth Banach space. Finally, we also apply our results to the problem of finding zeros of B-monotone mappings and maximal monotone operators. The results presented in this paper generalize and improve some well-known results in the literature. ฉ 2011 Saewan and Kumam; licensee Springer.

Keywords

System of generalized mixed equilibrium problems