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 and Siwaporn Saewan

Journal of Applied Mathematics, 2012, vol. 2012, issue 1

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 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.

Date: 2012
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https://doi.org/10.1155/2012/750732

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2012:y:2012:i:1:n:750732

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