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Abstract and Applied Analysis
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Abstract and Applied Analysis
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https://dx.doi.org/10.1155/201...
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Claim

A Sharp Double Inequality between Harmonic and Identric Means

A sharp double inequality between harmonic and identric means
descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2011 English Publisher:WileyJournal:Abstract and Applied Analysis, volume 2,011 (issn: 1085-3375, eissn: 1687-0409, Copyright policy )
Authors: Yu-Ming Chu; Miao-Kun Wang; Zi-Kui Wang;

doi: 10.1155/2011/657935

A Sharp Double Inequality between Harmonic and Identric Means

Abstract

We find the greatest value p and the least value q in (0,1/2) such that the double inequality H(pa + (1 − p)b, pb + (1 − p)a) < I(a, b) < H(qa + (1 − q)b, qb + (1 − q)a) holds for all a, b > 0 with a ≠ b. Here, H(a, b), and I(a, b) denote the harmonic and identric means of two positive numbers a and b, respectively.

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Keywords

identric mean, QA1-939, Inequalities for sums, series and integrals, harmonic mean, Mathematics, Means

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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Average
Top 10%
gold