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Some results on stability and on characterization of \(K\)-convexity of set-valued functions. (English) Zbl 0786.26016

The aim of this note is twofold. First, it is proved that the \(K\)- convexity of nonempty set-valued functions (in the finite-dimensional setting) is stable in the sense of Hyers and Ulam. This result generalizes and extends most of the results known about the stability of convex functions.
The second goal is the characterization of nonempty compact set-valued \(K\)-convex functions in terms of \(K\)-\(t\)-convexity and \(K\)- quasiconvexity.

MSC:

26E25 Set-valued functions
26B25 Convexity of real functions of several variables, generalizations
54C60 Set-valued maps in general topology
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