ON THE CONTINUITY AND DIFFERENTIABILITY OF THE IMPLICIT FUNCTIONS FOR GENERALIZED EQUATIONS

Abstract

 The aim of this paper is to show that the existence, continuity and differentiabilty of the implicit functions can be proved at the same time, using one sequence of succesive approximations of a mapping of two variables. The proof from this paper unifies methods used in the study of local stability and sensitivity of the solutions of integral equations [7], variational inequalities and nonsmooth generalized equations [1, 2, 5, 6]. We will prove the continuous differentiability of the solution mapping mapping in a neighborhood of a fixed parameter l₀.