Iterative approximation of a common solution of a split generalized equilibrium problem and a fixed point problem for nonexpansive semigroup

Abstract

Purpose: In this paper, we introduce and study an iterative method to approximate a common solution of a split generalized equilibrium problem and a fixed point problem for a nonexpansive semigroup in real Hilbert spaces. Methods: We prove a strong convergence theorem of the iterative algorithm in Hilbert spaces under certain mild conditions. Results: We obtain a strong convergence result for approximating a common solution of a split generalized equilibrium problem and a fixed point problem for a nonexpansive semigroup in real Hilbert spaces, which is a unique solution of a variational inequality problem. Further, we obtain some consequences of our main result. Conclusions: The results presented in this paper are the supplement, extension, and generalization of results in the study of Plubtieng and Punpaeng and that of Cianciaruso et al. The approach of the proof given in this paper is also different.