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A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities

Author

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  • Thanyarat Jitpeera
  • Poom Kumam

Abstract

We introduce a new general iterative method for finding a common element of the set of solutions of fixed point for nonexpansive mappings, the set of solution of generalized mixed equilibrium problems, and the set of solutions of the variational inclusion for a β -inverse-strongly monotone mapping in a real Hilbert space. We prove that the sequence converges strongly to a common element of the above three sets under some mild conditions. Our results improve and extend the corresponding results of Marino and Xu (2006), Su et al. (2008), Klin-eam and Suantai (2009), Tan and Chang (2011), and some other authors.

Suggested Citation

  • Thanyarat Jitpeera & Poom Kumam, 2011. "A General Iterative Algorithm for Generalized Mixed Equilibrium Problems and Variational Inclusions Approach to Variational Inequalities," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2011, pages 1-25, April.
    • Handle: RePEc:hin:jijmms:619813
    DOI: 10.1155/2011/619813
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    Cited by:

    1. 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).
    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, John Wiley & Sons, vol. 2012(1).
    3. Tanom Chamnarnpan & Poom Kumam, 2012. "Iterative Algorithms for Solving the System of Mixed Equilibrium Problems, Fixed‐Point Problems, and Variational Inclusions with Application to Minimization Problem," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).

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