Strong convergence theorems for fixed point problems, variational inequality problems, and equilibrium problems
Zhangsong Yao, Yeong‐Cheng Liou, Li-Jun Zhu, Ching‐Hua Lo, Chen Wu · Journal of Inequalities and Applications · 2015
In this paper, we first introduce an iterative algorithm for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions of an equilibrium problem, and the solution set of the variational inequality problem for a monotone mapping in a real Hilbert space. Furthermore, we prove that the proposed iterative algorithm converges strongly to a common element of the above three sets under some mild conditions.