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2012 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
Preedaporn Kanjanasamranwong, Poom Kumam, Siwaporn Saewan
J. Appl. Math. 2012(SI03): 1-19 (2012). DOI: 10.1155/2012/750732

Abstract

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 andstrictly 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 improvethe result of Chang et al., (2012), and some others.

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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." J. Appl. Math. 2012 (SI03) 1 - 19, 2012. https://doi.org/10.1155/2012/750732

Information

Published: 2012
First available in Project Euclid: 3 January 2013

zbMATH: 1323.47071
MathSciNet: MR2948090
Digital Object Identifier: 10.1155/2012/750732

Rights: Copyright © 2012 Hindawi

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Vol.2012 • No. SI03 • 2012
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