On concave and midpoint concave set-valued functions. (English) Zbl 0642.39006
In the first part of this paper the author considers three kinds of concavity for set-valued functions and gives some connections between them. In the second part he presents sufficient conditions for midpoint concave and concave set-valued functions to be continuous with respect to the Hausdorff topology. These results are analogous to classical theorems concerning midpoint convex real-valued functions.
Reviewer: I.Raşa
MSC:
39B72 | Systems of functional equations and inequalities |
26B25 | Convexity of real functions of several variables, generalizations |
26E25 | Set-valued functions |