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Zbl 1188.49027
Ceng, L.C.; Wong, N.C.
Viscosity approximation methods for equilibrium problems and fixed point problems of nonlinear semigroups. (English)
[J] Taiwanese J. Math. 13, No. 5, 1497-1513 (2009). ISSN 1027-5487

Summary: The purpose of this paper is to suggest and analyze a new 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 common fixed points of a commutative family of nonexpansive mappings in a Hilbert space. Then we prove a strong convergence theorem which is connected with the results of {\it S. Takahashi} and {\it W. Takahashi} [J. Math. Anal. Appl. 331, No.~1, 506--515 (2007; Zbl 1122.47056)] and {\it Y. Yao} and {\it M. A. Noor} [J. Math. Anal. Appl. 325, No.~2, 776--787 (2007; Zbl 1115.49024)]. Using this result, we obtain two corollaries which improve and extend their results.

MSC 2000:: *49L25 Viscosity solutions
49J40 Variational methods including variational inequalities
90C29 Multi-objective programming, etc.
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: viscosity approximation method; equilibrium problem; common fixed point; nonexpansive mapping; strong convergence; uniformly asymptotic regularity

Citations: Zbl 1122.47056; Zbl 1115.49024

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