Some inverse mapping theorems

Abstract

We prove several first and high order inverse mapping theorems for set-valued maps from a complete metric space to a Banach space and study the stability of the open mapping principle. The obtained results allow to investigate questions of controllability of finite and infinite dimensional control systems, necessary conditions for optimality, implicit function theorem, stability of constraints with respect to a parameter. Applications to problems of optimization, control theory and nonsmooth analysis are provided.

Résumé

On démontre des théorèmes d’inversion locale d’ordre quelconque pour des correspondances définies sur un espace métrique complet. Les résultats sont appliqués à quelques problèmes des contrôles.