Maximum theorems with strict quasi-concavity and applications

In this paper, we first prove the strict quasi-concavity of maximizing functions, and next, using a generalization of the KKM theorem, we prove two maximum theorems without assuming the upper semicontinuity. As an application, using a common fixed point theorem, the existence theorem of social equilibrium is obtained. Finally, we shall give two illustrative examples of systems of constrained optimization problems.