An Approximation algorithm for the combination of G-variational inequality and fixed point problems

Abstract

Abstract In this paper, we introduce a new problem is called the combination of G-variational inequality problem in a Hilbert space endowed with graphs and an iterative scheme to find a common element of the set of fixed points of a G-nonexpansive mapping and the solution set of the proposed problem. Under suitable assumptions, a strong convergence theorem has been proved in the framework of a Hilbert space endowed with graphs. Applying our main result, we solve the G-minimization problem. We also give examples to support our main results. Mathematics Subject Classification (2010). 47H09, 47H10, 90C99. Keywords. the combination of G-variational inequality problems, fixed point problem, G-inverse strongly monotone mapping. Mathematics Subject Classification (2010). 47H09, 47H10, 90C99.