Somayeh Mirzadeh - Department of Mathematics, Hormozgan university, Bandar abbas, Iran
samaneh bahrami - Department of Mathematics, Shahid Bahonar University of Kerman, Kerman, Iran

In this paper, we first study the non-positive decreasing and inverse co-radiantfunctions defined on a real locally convex topological vector space X. Next, we characterize non-positive increasing, co-radiant and quasi-concave functions over X. In fact, we examine abstract concavity, upper support set and superdifferential of this class of functions by applying a type of duality. Finally, we present abstract concavity of extended real valued increasing, co-radiant and quasi-concave functions.

Abstract concavity, Duality, Co-radiant function, Quasi-concave function, Upper support set