Viscosity approximation methods for equilibrium problems and fixed point problems of nonexpansive mappings and inverse-strongly monotone mappings
Jianmin Song, Shenghua Wang, Haiyun Zhou · Methods and Applications of Analysis · 2007
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].