A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space

A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space

The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f-projection operator for finding a common solution of fixed-point problem of a totally quasi-ϕ-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and str...

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Main Authors: Preedaporn Kanjanasamranwong, Poom Kumam, Siwaporn Saewan
Format: Article
Language:English
Published: Hindawi Limited 2012-01-01
Series:Journal of Applied Mathematics
Online Access:http://dx.doi.org/10.1155/2012/750732
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spelling doaj-94834608c8c04014bf676fcdd39ddff72020-11-24T23:12:17ZengHindawi LimitedJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/750732750732A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach SpacePreedaporn Kanjanasamranwong0Poom Kumam1Siwaporn Saewan2Department of Mathematics and Statistics, Faculty of Science, Thaksin University (TSU), Pa Phayom, Phatthalung 93110, ThailandDepartment of Mathematics, Faculty of Science, King Mongkut’s University of Technology Thonburi (KMUTT), Bangmod, Bangkok 10140, ThailandDepartment of Mathematics and Statistics, Faculty of Science, Thaksin University (TSU), Pa Phayom, Phatthalung 93110, ThailandThe purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f-projection operator for finding a common solution of fixed-point problem of a totally quasi-ϕ-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve the result of Chang et al., (2012), and some others.http://dx.doi.org/10.1155/2012/750732
collection DOAJ
language English
format Article
sources DOAJ
author Preedaporn Kanjanasamranwong
Poom Kumam
Siwaporn Saewan
spellingShingle Preedaporn Kanjanasamranwong
Poom Kumam
Siwaporn Saewan
A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space
Journal of Applied Mathematics
author_facet Preedaporn Kanjanasamranwong
Poom Kumam
Siwaporn Saewan
author_sort Preedaporn Kanjanasamranwong
title A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space
title_short A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space
title_full A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space
title_fullStr A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space
title_full_unstemmed A Modified Halpern-TypeIterative Method of a System of Equilibrium Problems and a Fixed Point for a Totally Quasi-ϕ-Asymptotically Nonexpansive Mapping in a Banach Space
title_sort modified halpern-typeiterative method of a system of equilibrium problems and a fixed point for a totally quasi-ϕ-asymptotically nonexpansive mapping in a banach space
publisher Hindawi Limited
series Journal of Applied Mathematics
issn 1110-757X
1687-0042
publishDate 2012-01-01
description The purpose of this paper is to introduce the modified Halpern-type iterative method by the generalized f-projection operator for finding a common solution of fixed-point problem of a totally quasi-ϕ-asymptotically nonexpansive mapping and a system of equilibrium problems in a uniform smooth and strictly convex Banach space with the Kadec-Klee property. Consequently, we prove the strong convergence for a common solution of above two sets. Our result presented in this paper generalize and improve the result of Chang et al., (2012), and some others.
url http://dx.doi.org/10.1155/2012/750732
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