INVERSE FUNCTION THEOREM WITH STRONG METRIC REGULARITY

Abstract

Abstract. In this paper we prove an extension of the contraction mapping principle for single-valued mappings dealing with more general assumptions containing modulus instead of pseudo-contractive functions. In [4] A. L. Dontchev and R.T. Rockaffelar supposethe strong metric regularity of set-valued mapping  and the Lipschitz continuity of the function  with given nonnegative constants and prove the strong metric regularity of  while we assume the properties of  and  with modulus functions and prove a generalization of their result.