On some optimization problems in not necessarily locally convex space

Abstract

In this note, by using O. Hadžić's generalization of a fixed point theorem of Himmelberg, we prove a non - cooperative equilibrium existence theorem in non - compact settings and a generalization of an existence theorem for non - compact infinite optimization problems, all in not necessarily locally convex spaces.

Keywords

• set valued mapping
• quasi - convex map
• non-cooperative equilibrium