Bilevel equilibrium problems with lower and upper bounds in locally convex Hausdorff topological vector spaces

Abstract

In this paper, we introduce a new class of bilevel equilibrium problems with lower and upper bounds in locally convex Hausdorff topological vector spaces and establish some conditions for the existence of solutions to these problems using the Kakutani-Fan-Glicksberg fixed-point theorem. Then, we establish generic stability of set-valued mappings and we show the set of essential points of a map is a dense residual subset of a (Hausdorff) metric space of set-valued maps for bilevel equilibrium problems with lower and upper bounds. The results presented in the paper are new and extend the main results given by some authors in the literature.