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A General Composite Algorithms for Solving General Equilibrium Problems and Fixed Point Problems in Hilbert Spaces

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Listed:
  • Rattanaporn Wangkeeree
  • Uthai Kamraksa
  • Rabian Wangkeeree

Abstract

We introduce a general composite algorithm for finding a common element of the set of solutions of a general equilibrium problem and the common fixed point set of a finite family of asymptotically nonexpansive mappings in the framework of Hilbert spaces. Strong convergence of such iterative scheme is obtained which solving some variational inequalities for a strongly monotone and strictly pseudocontractive mapping. Our results extend the corresponding recent results of Yao and Liou (2010).

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2011:y:2011:i:1:n:976412
    DOI: 10.1155/2011/976412
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    References listed on IDEAS

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    1. 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.
    2. Jian-Wen Peng & Soon-Yi Wu & Jen-Chih Yao, 2010. "A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed‐Point Problems, and Variational Inequalities," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    3. Chakkrid Klin-eam & Suthep Suantai & Wataru Takahashi, 2009. "Strong Convergence of Generalized Projection Algorithms for Nonlinear Operators," Abstract and Applied Analysis, John Wiley & Sons, vol. 2009(1).
    4. Chakkrid Klin-eam & Suthep Suantai & Wataru Takahashi, 2009. "Strong Convergence of Generalized Projection Algorithms for Nonlinear Operators," Abstract and Applied Analysis, Hindawi, vol. 2009, pages 1-18, November.
    5. Wanpen Chantarangsi & Chaichana Jaiboon & Poom Kumam, 2010. "A Viscosity Hybrid Steepest Descent Method for Generalized Mixed Equilibrium Problems and Variational Inequalities for Relaxed Cocoercive Mapping in Hilbert Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
    6. Jian-Wen Peng & Soon-Yi Wu & Jen-Chih Yao, 2010. "A New Iterative Method for Finding Common Solutions of a System of Equilibrium Problems, Fixed-Point Problems, and Variational Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2010, pages 1-27, August.
    7. Yonghong Yao & Yeong-Cheng Liou, 2010. "Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems," Abstract and Applied Analysis, John Wiley & Sons, vol. 2010(1).
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