Existence and modification of halpern-mann iterations for fixed point and generalized mixed equilibrium problems with a bifunction defined on the dual space

Journal article

Authors/Editors

POOM KUMAM

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Publication Details

Author list: Phuangphoo P., Kumam P.

Publisher: Hindawi

Publication year: 2013

Journal: Journal of Applied Mathematics (1110-757X)

Volume number: 2013

ISSN: 1110-757X

eISSN: 1687-0042

URL: https://www.scopus.com/inward/record.uri?eid=2-s2.0-84888865169&doi=10.1155%2f2013%2f753096&partnerID=40&md5=ccebfd4b571550a253660d743e2d706d

Languages: English-Great Britain (EN-GB)

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Abstract

We study and establish the existence of a solution for a generalized mixed equilibrium problem with a bifunction defined on the dual space of a Banach space. Furthermore, we also modify Halpern-Mann iterations for finding a common solution of a generalized mixed equilibrium problem and a fixed point problem. Under suitable conditions of the purposed iterative sequences, the strong convergence theorems are established by using sunny generalized nonexpansive retraction in Banach spaces. Our results extend and improve various results existing in the current literature. ฉ 2013 Pongrus Phuangphoo and Poom Kumam.

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