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A New General Iterative Method for Solution of a New General System of Variational Inclusions for Nonexpansive Semigroups in Banach Spaces

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  • Pongsakorn Sunthrayuth
  • Poom Kumam

Abstract

We introduce a new general system of variational inclusions in Banach spaces and propose a new iterative scheme for finding common element of the set of solutions of the variational inclusion with set-valued maximal monotone mapping and Lipschitzian relaxed cocoercive mapping and the set of fixed point of nonexpansive semigroups in a uniformly convex and 2-uniformly smooth Banach space. Furthermore, strong convergence theorems are established under some certain control conditions. As applications, finding a common solution for a system of variational inequality problems and minimization problems is given.

Suggested Citation

  • 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.
    • Handle: RePEc:hin:jnljam:187052
    DOI: 10.1155/2011/187052
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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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