New (Probabilistic) Derivation of Diaz-Metcalf and Pólya-Szegő Inequalities and Consequences

Pogány, Tibor K (2004) New (Probabilistic) Derivation of Diaz-Metcalf and Pólya-Szegő Inequalities and Consequences. Research report collection, 7 (1).


Classical inequalities of Diaz - Metcalf and Pólya - Szegő are generalized to probabilistic setting which covers the initial deterministic (both discrete and integral) variants. From these two inequalities, by the probabilistic derivation method further well - known inequalities are obtained (that ones by Kantorovich, Rennie and Schweitzer).

Item type Article
Subjects Historical > FOR Classification > 0101 Pure Mathematics
Historical > FOR Classification > 0104 Statistics
Current > Collections > Research Group in Mathematical Inequalities and Applications (RGMIA)
Keywords almost surely bounded random variable, Diaz-Metcalf inequality, discrete inequality, integral inequality, Kantorovich inequality, mathematical expectation, Polya-Szego inequality, Rennie inequality, Schweitzer inequality
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