hasan barsam

In this paper, we study abstract convexity topical and sub-topical functions. We obtain some results on abstract convexity such as support set and subdierential in view of new elementary functions. Indeed, rst we show that the ICR and IR functions are dense in IPH functions then the topical function and sub-topical function on topological vector space by another elementary function is studied. These elementary functions lead to obtain similar results with easier proofs.