A general composite iterative method for generalized mixed equilibrium problems, variational inequality problems and optimization problems
Jong Soo Jung · Journal of Inequalities and Applications · 2011
In this article, we introduce a new general composite iterative scheme for finding a common element of the set of solutions of a generalized mixed equilibrium problem, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions of a variational inequality problem for an inverse-strongly monotone mapping in Hilbert spaces.It is shown that the sequence generated by the proposed iterative scheme converges strongly to a common element of the above three sets under suitable control conditions, which solves a certain optimization problem.The results of this article substantially improve, develop, and complement the previous well-known results in this area.