Methods and Applications of Analysis
Volume 14 (2007)
Viscosity approximation methods for equilibrium problems and fixed point problems of nonexpansive mappings and inverse-strongly monotone mappings
Pages: 405 – 420
In this paper, we introduce an iterative scheme by viscosity approximation method for obtaining a common element of the set of solutions of an equilibrium problem and the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality for an inverse-strongly monotone mapping in a Hilbert space. We obtain a strong convergence which improves and extends S. Takahashi and W. Takahashi's result [S. Takahashi, W. Takahashi, Viscosity approximation methods for equilibrium problems and fixed point problems in Hilbert spaces, J. Math. Anal. Appl. 331 (2007) 506-515].
viscosity approximation method; equilibrium problem; inverse-strongly monotone mapping; nonexpansive mapping; variational inequality
2010 Mathematics Subject Classification