Enlargements of Monotone Operators Determined by Representing Functions

In this paper, we study a new enlargement of subdifferential for any proper lower semicontinuous function. We know that "-subdifferential of any proper lower semicontinuous function is an enlargement of its subfifferential and any point from the graph of "- subdifferential can be approximated by a point from the graph of subfifferential. 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 subdifferentials, the relation between this new enlargement and the "- subdifferential.