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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

Author

Listed:
  • Poom Kumam
  • Phayap Katchang

Abstract

We introduce an iterative algorithm for finding a common element of the set of solutions of a system of mixed equilibrium problems, the set of solutions of a general system of variational inequalities for Lipschitz continuous and relaxed cocoercive mappings, the set of common fixed points for nonexpansive semigroups, and the set of common fixed points for an infinite family of strictly pseudocontractive mappings in Hilbert spaces. Furthermore, we prove a strong convergence theorem of the iterative sequence generated by the proposed iterative algorithm under some suitable conditions which solves some optimization problems. Our results extend and improve the recent results of Chang et al. (2010) and many others.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnljam:v:2012:y:2012:i:1:n:414831
    DOI: 10.1155/2012/414831
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    References listed on IDEAS

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    1. 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, Hindawi, vol. 2012, pages 1-30, February.
    2. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-39, December.
    3. Pongsakorn Sunthrayuth & Poom Kumam, 2012. "A System of Generalized Mixed Equilibrium Problems, Maximal Monotone Operators, and Fixed Point Problems with Application to Optimization Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    4. 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.
    5. 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).
    6. 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).
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    Cited by:

    1. 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).
    2. Jong Soo Jung, 2012. "Weak Convergence Theorems for Strictly Pseudocontractive Mappings and Generalized Mixed Equilibrium Problems," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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