Abstract convexity of extended real valued increasing and positively homogeneous functions. (English) Zbl 1206.26016
Summary: We examine abstract convexity of extended real valued increasing and positively homogeneous functions defined on ordered topological vector spaces.
We also study many other associated properties like the description of support set, polar function and subdifferential. Finally, we give a characterization for upward sets in a very general setting.
We also study many other associated properties like the description of support set, polar function and subdifferential. Finally, we give a characterization for upward sets in a very general setting.
MSC:
| 26A48 | Monotonic functions, generalizations |
| 52A07 | Convex sets in topological vector spaces (aspects of convex geometry) |
| 26A51 | Convexity of real functions in one variable, generalizations |
