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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

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  • Pongsakorn Sunthrayuth
  • Poom Kumam

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.

Suggested Citation

  • Pongsakorn Sunthrayuth & Poom Kumam, 2012. "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 Prob," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-30, February.
    • Handle: RePEc:hin:jnlaaa:979870
    DOI: 10.1155/2012/979870
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