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Ohlin type theorem and its applications for strongly convex set-valued maps

A version of the Ohlin theorem for strongly convex set-valued maps is presented. As an application counterparts of the Jensen, converse Jensen and Hermite-Hadamard inequalities for strongly convex set-valued maps are proved in a simple unified way.

Ohlin’s lemma ; strongly convex set-valued maps ; Jensen inequality ; converse Jensen inequality ; Hermite-Hadamard inequalities

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