H. Eshaghi Kenari - Department of Mathematics and Statics, University of Birjand, Birjand, Iran.
A. Asadi - Department of Mathematics and Statics, University of Birjand, Birjand, Iran.
MR. Miri - Department of Mathematics and Statics, University of Birjand, Birjand, Iran.

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.

Abstract sub-differential, Abstract monotone operator, Enlargement, ε- Abstract sub-differential