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A new (probabilistic) proof of the Diaz-Metcalf and Pólya-Szego inequalities and some applications

Author: Tibor K. Pogány
Translated by: The author
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 70 (2004).
Journal: Theor. Probability and Math. Statist. 70 (2005), 113-122
MSC (2000): Primary 26D15, 60E15
Published electronically: August 12, 2005
MathSciNet review: 2109828
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Abstract: The Diaz-Metcalf and Pólya-Szego inequalities are proved in the probabilistic setting. These results generalize the classical case for both sums and integrals. Using these results we obtain some other well-known inequalities in the probabilistic setting, namely the Kantorovich, Rennie, and Schweitzer inequalities.

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Additional Information

Tibor K. Pogány
Affiliation: Faculty of Maritime Studies, University of Rijeka, Studentska 2, 51000 Rijeka, Croatia

Keywords: Almost surely bounded random variable, Diaz--Metcalf inequality, discrete inequality, integral inequality, Kantorovich inequality, mathematical expectation, P\'olya--Szeg\H o inequality, Rennie inequality, Schweitzer inequality
Received by editor(s): March 20, 2002
Published electronically: August 12, 2005
Article copyright: © Copyright 2005 American Mathematical Society

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