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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

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  • 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 M," Journal of Applied Mathematics, Hindawi, vol. 2012, pages 1-35, May.
    • Handle: RePEc:hin:jnljam:414831
    DOI: 10.1155/2012/414831
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    Cited by:

    1. Bashir Ali & G. C. Ugwunnadi, 2012. "Convergence Theorem for a Family of Generalized Asymptotically Nonexpansive Semigroup in Banach Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2012, pages 1-16, July.

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