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2012 A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems
Pongsakorn Sunthrayuth, Poom Kumam
Abstr. Appl. Anal. 2012(SI12): 1-39 (2012). DOI: 10.1155/2012/316276

Abstract

We introduce a new iterative algorithm for finding a common element of the set of solutions of a system of generalized mixed equilibrium problems, zero set of the sum of a maximal monotone operators and inverse-strongly monotone mappings, and the set of common fixed points of an infinite family of nonexpansive mappings with infinite real number. Furthermore, we prove under some mild conditions that the proposed iterative algorithm converges strongly to a common element of the above four sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator. The results presented in the paper improve and extend the recent ones announced by many others.

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Pongsakorn Sunthrayuth. Poom Kumam. "A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems." Abstr. Appl. Anal. 2012 (SI12) 1 - 39, 2012. https://doi.org/10.1155/2012/316276

Information

Published: 2012
First available in Project Euclid: 15 February 2012

zbMATH: 1232.49037
MathSciNet: MR2872300
Digital Object Identifier: 10.1155/2012/316276

Rights: Copyright © 2012 Hindawi

Vol.2012 • No. SI12 • 2012
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