Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space

Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space

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...

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Main Authors: Pongrus Phuangphoo, Poom Kumam
Format: Article
Language:English
Published: Hindawi Limited 2013-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2013/753096
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spelling doaj-27362287434c4edab544513dab7ea0a52020-11-25T00:56:34ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/753096753096Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual SpacePongrus Phuangphoo0Poom Kumam1Department of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok 10140, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bang Mod, Thung Khru, Bangkok 10140, ThailandWe 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.http://dx.doi.org/10.1155/2013/753096
collection DOAJ
language English
format Article
sources DOAJ
author Pongrus Phuangphoo
Poom Kumam
spellingShingle Pongrus Phuangphoo
Poom Kumam
Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space
Journal of Applied Mathematics
author_facet Pongrus Phuangphoo
Poom Kumam
author_sort Pongrus Phuangphoo
title Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space
title_short Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space
title_full Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space
title_fullStr Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space
title_full_unstemmed Existence and Modification of Halpern-Mann Iterations for Fixed Point and Generalized Mixed Equilibrium Problems with a Bifunction Defined on the Dual Space
title_sort existence and modification of halpern-mann iterations for fixed point and generalized mixed equilibrium problems with a bifunction defined on the dual space
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2013-01-01
description 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.
url http://dx.doi.org/10.1155/2013/753096
work_keys_str_mv AT pongrusphuangphoo existenceandmodificationofhalpernmanniterationsforfixedpointandgeneralizedmixedequilibriumproblemswithabifunctiondefinedonthedualspace
AT poomkumam existenceandmodificationofhalpernmanniterationsforfixedpointandgeneralizedmixedequilibriumproblemswithabifunctiondefinedonthedualspace
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