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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

Author

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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, John Wiley & Sons, vol. 2011(1).
    • Handle: RePEc:wly:jnljam:v:2011:y:2011:i:1:n:187052
    DOI: 10.1155/2011/187052
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    References listed on IDEAS

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    1. Ram U. Verma, 2004. "A -monotonicity and applications to nonlinear variational inclusion problems," International Journal of Stochastic Analysis, Hindawi, vol. 2004, pages 1-3, January.
    2. 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.
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    Cited by:

    1. 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).
    2. 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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