A Strong Convergence Theorem by a New Hybrid Method for an Equilibrium Problem with Nonlinear Mappings in a Hilbert Space
Author
Shinzato, Rinko
Takahashi, Wataru
Abstract
In this paper, we prove a strong convergence theorem for finding a common element of the set of solutions of an equilibrium problem, the set of solutions of the variational inequality for a monotone mapping and the set of fixed points of a nonexpansive mapping in a Hilbert space by using a new hybrid method. Using this theorem, we obtain three new results for finding a solution of an equilibrium problem, a solution of the variational inequality for a monotone mapping and a fixed point of a nonexpansive mapping in a Hilbert space.