An iterative approximation of common solutions of split generalized vector mixed equilibrium problem and some certain optimization problems

Abstract

In this paper, we study the problem of finding a common solution of split generalized vector mixed equlibrium problem (SGVMEP), fixed point problem (FPP) and variational inequality problem (VIP). We propose an inertial-type iterative algorithm, which uses a projection onto a feasible set and a linesearch, which can be easily calculated. We prove a strong convergence of the sequence generated by the proposed algorithm to a common solution of SGVMEP, fixed point of a quasi-ϕ\phi -nonexpansive mapping and VIP for a general class of monotone mapping in 2-uniformly convex and uniformly smooth Banach space E1{E}_{1} and a smooth, strictly convex and reflexive Banach space E2{E}_{2}. Some numerical examples are presented to illustrate the performance of our method. Our result improves some existing results in the literature.

Keywords

• split feasibility problem
• vector equilibrium problem
• generalized mixed equilibrium problem
• quasi-monotone mapping
• strong convergence
• banach space
• 47h06
• 47h09
• 46n10