A Study of Downward Sets withp-Functions
H. Mohebi, Vahid Momenaei Kermani · Numerical Functional Analysis and Optimization · 2009
In this paper, we study downward sets and increasing functions in a topological vector space and their similarities to the convex sets and convex functions. It will be shown that a very special increasing function, namely, the p-function, can give a geometric interpretation for separating downward sets from outside points. Also, this function can be used to approximate topical functions in the framework of abstract convexity.