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Relaxed Iterative Algorithms for Generalized Mixed Equilibrium Problems with Constraints of Variational Inequalities and Variational Inclusions

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  • Lu-Chuan Ceng
  • Chi-Ming Chen
  • Ching-Feng Wen
  • Chin-Tzong Pang

Abstract

We introduce and analyze a relaxed extragradient-like viscosity iterative algorithm for finding a solution of a generalized mixed equilibrium problem with constraints of several problems: a finite family of variational inequalities for inverse strongly monotone mappings, a finite family of variational inclusions for maximal monotone and inverse strongly monotone mappings, and a fixed point problem of infinitely many nonexpansive mappings in a real Hilbert space. Under some suitable conditions, we derive the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems which also solves a variational inequality problem.

Suggested Citation

  • Lu-Chuan Ceng & Chi-Ming Chen & Ching-Feng Wen & Chin-Tzong Pang, 2014. "Relaxed Iterative Algorithms for Generalized Mixed Equilibrium Problems with Constraints of Variational Inequalities and Variational Inclusions," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-25, March.
    • Handle: RePEc:hin:jnlaaa:345212
    DOI: 10.1155/2014/345212
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