• Journal of the Chungcheong Mathematical Society
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• v.27 no.2
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• pp.165-172
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• 2014

In this paper, we derive some valuable inequalities of Rado's and Poponov's types on the open interval of positive real numbers, and then show weighted generalizations of Rado's and Poponov's inequalities on the set of positive real numbers equipped with compactly supported probability measure.

• The Pure and Applied Mathematics
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• v.7 no.1
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• pp.1-6
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• 2000

An extension of $H\"{o}lder's$ inequality whose discrete form is described as follows is given. Let $\nu$ be a positive measure on a space Y, $\nu(Y)\;\neq\;0$, and let $f_{j}$(j = 1,2,...,n) be positive ν-integrable functions on Y. If ${\alpha}_j$ > 0(j = 1,2,...,n) and ${\beta}_j$(j = 1,2,...,k < n) are related to be (equation omitted) then (equation omitted).