Some open mapping theorems for set-valued maps and application

Abstract

In this paper we present some results concerning with the open mapping theorem and the inverse mapping theorem for set-valued mapping. These results are applied to study the controllability for finite dimensional control system. They are given by Frankowska in [2], however most of them did not be proved in full detail. In here we present with the detail in proof.

            Keywords: Open mapping theorem, first order inverse mapping theorem, controllability, optimality.