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Theory of Probability and Mathematical Statistics
Theory of Probability and Mathematical Statistics
ISSN 1547-7363(online) ISSN 0094-9000(print)

 

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 | References | Similar Articles | Additional Information

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
Email: poganj@brod.pfri.hr

DOI: http://dx.doi.org/10.1090/S0094-9000-05-00635-6
PII: S 0094-9000(05)00635-6
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