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Iterative Algorithms for Systems of Generalized Equilibrium Problems with the Constraints of Variational Inclusion and Fixed Point Problems

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  • Lu-Chuan Ceng
  • Abdul Latif
  • Abdullah E. Al-Mazrooei

Abstract

We introduce and analyze a hybrid extragradient-like viscosity iterative algorithm for finding a common solution of a systems of generalized equilibrium problems and a generalized mixed equilibrium problem with the constraints of two problems: 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 prove the strong convergence of the sequence generated by the proposed algorithm to a common solution of these problems.

Suggested Citation

  • Lu-Chuan Ceng & Abdul Latif & Abdullah E. Al-Mazrooei, 2014. "Iterative Algorithms for Systems of Generalized Equilibrium Problems with the Constraints of Variational Inclusion and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-24, March.
    • Handle: RePEc:hin:jnlaaa:540381
    DOI: 10.1155/2014/540381
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    Cited by:

    1. Mihai Postolache & Ashish Nandal & Renu Chugh, 2019. "Strong Convergence of a New Generalized Viscosity Implicit Rule and Some Applications in Hilbert Space," Mathematics, MDPI, vol. 7(9), pages 1-24, August.
    2. Lu-Chuan Ceng & Mihai Postolache & Xiaolong Qin & Yonghong Yao, 2018. "System of Variational Inclusions and Fixed Points of Pseudocontractive Mappings in Banach Spaces," Mathematics, MDPI, vol. 7(1), pages 1-14, December.

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