Refinements of the Converse Hölder and Minkowski Inequalities

Josip Pečarić, Jurica Perić and Sanja Varošanec
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Josip Pečarić: Peoples Friendship University of Russia (RUDN University), 6 Miklukho-Maklaya Str., 117198 Moscow, Russia
Jurica Perić: Departments of Mathematics, Faculty of Science, University of Split, 21000 Split, Croatia
Sanja Varošanec: Department of Mathematics, University of Zagreb, 10000 Zagreb, Croatia

Mathematics, 2022, vol. 10, issue 2, 1-11

Abstract: We give a refinement of the converse Hölder inequality for functionals using an interpolation result for Jensen’s inequality. Additionally, we obtain similar improvements of the converse of the Beckenbach inequality. We consider the converse Minkowski inequality for functionals and of its continuous form and give refinements of it. Application on integral mixed means is given.

Keywords: Beckenbach’s inequality; converse inequality; Hölder’s inequality; mean; Minkowski’s inequality; mixed mean (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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