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Journal of Convex Analysis 29 (2022), No. 1, 221--229
Copyright Heldermann Verlag 2022

Ohlin Type Theorem and its Applications for Strongly Convex Set-Valued Maps

Milica Klaricic Bakula
Faculty of Science, University of Split, 21000 Split, Croatia

Kazimierz Nikodem
Dept. of Mathematics, University of Bielsko-Biala, 43-309 Bielsko-Biala, Poland

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.

Keywords: Ohlin's lemma, strongly convex set-valued maps, Jensen inequality, converse Jensen inequality, Hermite-Hadamard inequalities.

MSC: 26A51; 39B62, 54C60.

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