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Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings

Author

Listed:
  • L. C. Ceng

    (Shanghai Normal University
    Scientific Computing Key Laboratory of Shanghai Universities)

  • A. Petruşel

    (Babeş-Bolyai University)

  • J. C. Yao

    (National Sun Yat-sen University)

Abstract

Recently, O’Hara, Pillay and Xu (Nonlinear Anal. 54, 1417–1426, 2003) considered an iterative approach to finding a nearest common fixed point of infinitely many nonexpansive mappings in a Hilbert space. Very recently, Takahashi and Takahashi (J. Math. Anal. Appl. 331, 506–515, 2007) introduced an iterative scheme by the viscosity approximation method for finding a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space. In this paper, motivated by these authors’ iterative schemes, we introduce a new iterative approach to finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points of infinitely many nonexpansive mappings in a Hilbert space. The main result of this work is a strong convergence theorem which improves and extends results from the above mentioned papers.

Suggested Citation

  • L. C. Ceng & A. Petruşel & J. C. Yao, 2009. "Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings," Journal of Optimization Theory and Applications, Springer, vol. 143(1), pages 37-58, October.
    • Handle: RePEc:spr:joptap:v:143:y:2009:i:1:d:10.1007_s10957-009-9549-9
    DOI: 10.1007/s10957-009-9549-9
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