Solution of a class of equilibrium problems and variational inequalities in FC spaces

Abstract

In this paper, we study a class of mixed variational-like inequalities with respect to generalized weakly relaxed \(\eta {-}\alpha \) monotone mappings, involving nonlinear bifunctions, in finitely continuous topological space, in short FC space. Existence of the solution to the problem is established relaxing convexity and linearity condition by using generalized RKKM theorem. We have proposed a proximal iterative scheme using auxiliary principle technique. Solvability of the auxiliary variational inequality problem is established. Finally convergence of the iterates to the exact solution is proved. Some results with application to equilibrium problem are also discussed.