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- Title
Iterative Approaches to Solving Equilibrium Problems and Fixed Point Problems of Infinitely Many Nonexpansive Mappings.
- Authors
Ceng, L. C.; Petruşel, A.; Yao, J. C.
- Abstract
Recently, O’Hara, Pillay and Xu (Nonlinear Anal. 54, 1417–1426, ) 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, ) 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.
- Subjects
NONLINEAR operators; FIXED point theory; COINCIDENCE theory; NONEXPANSIVE mappings; INNER product spaces
- Publication
Journal of Optimization Theory & Applications, 2009, Vol 143, Issue 1, p37
- ISSN
0022-3239
- Publication type
Article
- DOI
10.1007/s10957-009-9549-9