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

L. C. Ceng (), A. Petruşel and J. C. Yao ()
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L. C. Ceng: Shanghai Normal University
A. Petruşel: Babeş-Bolyai University
J. C. Yao: National Sun Yat-sen University

Journal of Optimization Theory and Applications, 2009, vol. 143, issue 1, No 3, 37-58

Abstract: 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.

Keywords: Iterative approaches; Equilibrium problems; Fixed points; Nonexpansive mappings (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (5)

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DOI: 10.1007/s10957-009-9549-9

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