The shrinking projection method for common solutions of generalized mixed equilibrium problems and fixed point problems for strictly pseudocontractive mappings

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Kumam P., Jitpeera T.

Publisher: SpringerOpen

Publication year: 2011

Journal: Journal of Inequalities and Applications (1025-5834)

Volume number: 2011

ISSN: 1025-5834

eISSN: 1029-242X

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-79954987218&doi=10.1155%2f2011%2f840319&partnerID=40&md5=7ba8eceea6970afb360ef25f8e89e898

Languages: English-Great Britain (EN-GB)

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Abstract

We introduce the shrinking hybrid projection method for finding a common element of the set of fixed points of strictly pseudocontractive mappings, the set of common solutions of the variational inequalities with inverse-strongly monotone mappings, and the set of common solutions of generalized mixed equilibrium problems in Hilbert spaces. Furthermore, we prove strong convergence theorems for a new shrinking hybrid projection method under some mild conditions. Finally, we apply our results to Convex Feasibility Problems (CFP). The results obtained in this paper improve and extend the corresponding results announced by Kim et al. (2010) and the previously known results. ฉ 2011 Thanyarat Jitpeera and Poom Kumam.

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