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On Lipschitz midconvex multifunctions. (English) Zbl 1103.26011
It is proved that a normed space-valued midconvex multifunction with non-empty closed and bounded values, weakly upper bounded on a suitable ball of a normed space \(X\), is locally Lipschitzian. The proof utilizes some technical results, which are demonstrated in the first part of the paper. Moreover, as a corollary, a sufficient condition for Lipschitzianity of \(F\) on the whole of \(X\) is given.

MSC:
26A51 Convexity of real functions in one variable, generalizations
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References:
[1] NIKODEM K.: K-convex and K-concave set-valued functions. Zeszyty Nauk. Politech. Łódz. Mat. 559 (1989), 1-75.
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