Sublinear mappings and metric regularity

The metric regularity is a central concept in variational analysis. This concept is frequently used for the study of solutions to some generalized equations, to variational inequalities and to parametrized constraints systems. Fundamental theorems of this field are Eckart-Young's, Robinson-Ursescu's and Lyusternyk-Grave's theorem. They have applications in single valuedness functions theory and also in set-valuedmappings theory. The purpose of this article is to analize the metric regularity property of some sublinear applications.