Abstract
The purpose of this paper is to present an iterative scheme for finding a common element of the set of solutions to the variational inclusion problem with Lipschitzian and strongly monotone operator, fixed point of nonexpansive mappings and the set of solutions of an equilibrium problem in Hilbert spaces. Under suitable conditions, some strong convergence theorems for approximating this common elements are proved. The results presented in the paper improve and extend the main results of M. Tian [A general iterative algorithem for nonexpansive mappings in Hilbert space, Nonlinear Analysis, 73(2010)689-694] and Plubtemg and Sripard [A viscosity approximation method for finding common solution of variational inclusions, equilibrium problems, and fixed point problems in Hilbert spaces, Fixed Point Theory and Applications, vol.2009, Article ID 567147,20 pages].
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