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Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems

Author

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  • Yonghong Yao
  • Yeong-Cheng Liou

Abstract

The purpose of this paper is to solve the minimization problem of finding x ∗ such that x ∗ = arg min x ∈ Γ ‖ x ‖ 2 , where Γ stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one implicit and one explicit). Further, we prove that the proposed composite algorithms converge strongly to x ∗ .

Suggested Citation

  • Yonghong Yao & Yeong-Cheng Liou, 2010. "Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-19, October.
    • Handle: RePEc:hin:jnlaaa:763506
    DOI: 10.1155/2010/763506
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    Cited by:

    1. Rattanaporn Wangkeeree & Uthai Kamraksa & Rabian Wangkeeree, 2011. "A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2011(1).
    2. Wei Xu & Yuanheng Wang, 2012. "Strong Convergence of the Iterative Methods for Hierarchical Fixed Point Problems of an Infinite Family of Strictly Nonself Pseudocontractions," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).

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