An Iterative Method for Solving a System of Mixed Equilibrium Problems, System of Quasivariational Inclusions, and Fixed Point Problems of Nonexpansive Semigroups with Application to Optimization Problems

Pongsakorn Sunthrayuth and Poom Kumam

Abstract and Applied Analysis, 2012, vol. 2012, 1-30

Abstract:

We introduce a general implicit iterative scheme base on viscosity approximation method with a Ï•-strongly pseudocontractive mapping for finding a common element of the set of solutions for a system of mixed equilibrium problems, the set of common fixed point for a nonexpansive semigroup, and the set of solutions of system of variational inclusions with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mappings in Hilbert spaces. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets, which is a solution of the optimization problem related to a strongly positive bounded linear operator.

Date: 2012
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:979870

DOI: 10.1155/2012/979870

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