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On an inequality of Horst Alzer - MaRDI portal

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On an inequality of Horst Alzer (Q1815083)

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scientific article; zbMATH DE number 941336
Language Label Description Also known as
English
On an inequality of Horst Alzer
scientific article; zbMATH DE number 941336

    Statements

    title
    On an inequality of Horst Alzer (English)
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    publication date
    3 June 1997
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    review text
    Take \(n\) numbers in \(]0,1/2]\) then replace each by its reflexion on \(1/2\). The author offers new proofs of the results by \textit{H. Alzer} [Indigationes Math. 50, No. 4, 365-374 (1988; Zbl 0655.26010)] and by \textit{Ky Fan} [unpublished, quoted in \textit{E. F. Beckenbach} and \textit{R. Bellman}: ``Inequalities'' (1st ed. 1961; Zbl 0097.26502; 4th print 1983; Zbl 0513.26003), p. 5] that the difference of the arithmetic and geometric means of the reflected numbers is not greater and their quotient not smaller than that of the original numbers.
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    zbMATH Keywords
    inequality
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    arithmetic mean
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    geometric mean
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    reflected numbers
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    reviewed by
    János Aczél
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    Identifiers

    zbMATH DE Number
    941336
    0 references
    OpenAlex ID
    W1965717226
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