Enlargements of Monotone Operators Determined by Representing Functions

Abstract

In this paper, we study a new enlargement of subdifferential for any proper lower semicontinuous function. We know that ε-subdifferential of any proper lower semicontinuous function is an enlargement of its subfifferential and any point from the graph of ε-subdifferential can be approximated by a point from the graph of sub- fifferential. This nice property, apart from its theoretical importance, gives also the possibility to use the enlargement of subdifferentials in finding approximate solutions of inclusions determined by subdifferentials. We define a new enlargement and observe, in the case subdiffer- entials, the relation between this new enlargement and the ε-subdiffer- ential.