Name: On the Inequalities of Grüss–Čebyshev and Kantorovich: A Probabilistic Approach
Creator: Heinrich, Lothar
Keywords: Inequalities; stochastic orderings, Inequalities for sums, series and integrals, Kantorovich, Chebyshev and Grüss inequalities

On the inequalities of Grüss-Čebyshev and Kantorovich: a probabilistic approach

descriptionPublicationkeyboard_double_arrow_right Article 12 Oct 2020Embargo end date: 01 Jan 2020Publisher:European Mathematical Society - EMS - Publishing House GmbHJournal:Elemente der Mathematik, volume 75, pages 172-175 (issn: 0013-6018, eissn: 1420-8962,

Authors: Heinrich, Lothar;

doi: 10.4171/em/419 , 10.5169/seals-880894

On the Inequalities of Grüss–Čebyshev and Kantorovich: A Probabilistic Approach

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Abstract

Summary: First we recall the original form of inequalities found by P. L. Čebyshev in 1882, G. Grüss in 1935 and V. L. Kantorovich in 1948. Then we formulate generalized versions of these inequalities in the language of probability theory which allows to prove them by simple probabilistic arguments. A further moment inequality of this type rounds off this note.

Related Organizations

Universität Augsburg
Germany

Keywords

Inequalities; stochastic orderings, Inequalities for sums, series and integrals, Kantorovich, Chebyshev and Grüss inequalities

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