Enlargements of Abstract Monotone Operators Determind by Representing Functions

Abstract

In this paper, we study a new enlargement of abstract sub-differential for any IPH function. This nice property, apart from its theoretical importance, gives also the possibility to use the enlargement of abstract sub-differential in finding approximate solutions of inclusions determined by abstract sub-differentials. We define a new enlargement and observe, in the case abstract sub-differential, the relation between this new enlargement and the ε -abstract sub-differential.