Convergence analysis of hybrid projection with Cesàro mean method for the split equilibrium and general system of finite variational inequalities

Abstract

In this paper, we present a new iterative algorithm for finding a common element of three solution sets; (i) split equilibrium problem; (ii) general system of finite variational inequality problem; and (iii) fixed point problem. This algorithm is modified by hybrid method based on Cesàro mean in real Hilbert spaces. Furthermore, a strong convergent theorem is established and this theorem is the generalization of many previously known results in this research area. Finally, we study the rate of convergence of the iterative algorithm and some illustrative numerical examples are presented.