Abstract

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.

Author information

Contact details are reproduced from the original publication and may be historical.

Milica Klaricic Bakula

Faculty of Science, University of Split, 21000 Split, Croatia

milica@pmfst.hr

Kazimierz Nikodem

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

knikodem@ath.bielsko.pl

Keywords

  • Ohlin's lemma
  • strongly convex set-valued maps
  • Jensen inequality
  • converse Jensen inequality
  • Hermite-Hadamard inequalities

Mathematics Subject Classification

26A51; 39B62, 54C60

Suggested citation

M. Klaricic Bakula, K. Nikodem. “Ohlin Type Theorem and its Applications for Strongly Convex Set-Valued Maps.” Journal of Convex Analysis 29 (2022), No. 1, 221–229.

Copyright Heldermann Verlag 2022