on extended real valued quasi-concave functions

In this paper, we first study the non-positive decreasing and inverse co-radiant functions defined on a real locally convex topological vector space χ. next, we characterize non-positive increasing, co-radiant and quasi-concave functions over x. in fact, we examine abstract con- cavity, upper support set and superdi erential 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.