Vector parametric quasi-equilibrium problems for the sum of two set-valued mappings

Abstract

In this paper, we consider parametric quasi-equilibrium problems for the sum of two setvalued mappings. We present sufficient conditions for the existence of solution of these problems by using a generalized KKM-type theorem in topological vector spaces. Also, we obtain the equivalence between the existence of solution of these problems and scalar equilibrium problem, by a new scalarization.