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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 ϕ‐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 Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    • Handle: RePEc:wly:jnlaaa:v:2012:y:2012:i:1:n:979870
    DOI: 10.1155/2012/979870
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    References listed on IDEAS

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    1. Poom Kumam & Usa Hamphries & Phayap Katchang, 2011. "Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-28, September.
    2. Poom Kumam & Usa Hamphries & Phayap Katchang, 2011. "Common Solutions of Generalized Mixed Equilibrium Problems, Variational Inclusions, and Common Fixed Points for Nonexpansive Semigroups and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    3. Pongsakorn Sunthrayuth & Poom Kumam, 2011. "A New Composite General Iterative Scheme for Nonexpansive Semigroups in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-18, May.
    4. Pongsakorn Sunthrayuth & Poom Kumam, 2011. "A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2011(1).
    5. Pongsakorn Sunthrayuth & Poom Kumam, 2011. "A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces," Journal of Applied Mathematics, Hindawi, vol. 2011, pages 1-29, July.
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    Cited by:

    1. Poom Kumam & Phayap Katchang, 2012. "A System of Mixed Equilibrium Problems, a General System of Variational Inequality Problems for Relaxed Cocoercive, and Fixed Point Problems for Nonexpansive Semigroup and Strictly Pseudocontractive Mappings," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    2. Haitao Che & Meixia Li & Xintian Pan, 2012. "Convergence Theorems for Equilibrium Problems and Fixed‐Point Problems of an Infinite Family of ki‐Strictly Pseudocontractive Mapping in Hilbert Spaces," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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