Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:331

Article

Takahashi, Satoru ; Takahashi, Wataru

关键词: viscosity approximation method;    equilibrium problem;    fixed point;    nonexpansive mapping;   

DOI  :  10.1016/j.jmaa.2006.08.036

来源: Elsevier

【 摘 要 】

In this paper, we introduce 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. Then, we prove a strong convergence theorem which is connected with Combettes and Hirstoaga's result [PL. Combettes, S.A. Hirstoaga, Equilibrium programming in Hilbert spaces, J. Nonlinear Convex Anal. 6 (2005) 117-136] and Wittmann's result [R. Wittmann, Approximation of fixed points of nonexpansive mappings, Arch. Math. 58 (1992) 486-491]. Using this result, we obtain two corollaries which improve and extend their results. (C) 2006 Elsevier Inc. All rights reserved.

【 授权许可】

Free