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https://dx.doi.org/10.1155/201...
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Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means

Optimal lower power mean bound for the convex combination of harmonic and logarithmic means
descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2011 English Publisher:WileyJournal:Abstract and Applied Analysis, volume 2,011 (issn: 1085-3375, eissn: 1687-0409, Copyright policy )
Authors: Chu, Yu-Ming; Wang, Shan-Shan; Zong, Cheng;

doi: 10.1155/2011/520648

Optimal Lower Power Mean Bound for the Convex Combination of Harmonic and Logarithmic Means

Abstract

We find the least value λ ∈ (0, 1) and the greatest value p = p(α) such that αH(a, b) + (1 − α)L(a, b) > Mp(a, b) for α ∈ [λ, 1) and all a, b > 0 with a ≠ b, where H(a, b), L(a, b), and Mp(a, b) are the harmonic, logarithmic, and p‐th power means of two positive numbers a and b, respectively.

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Keywords

QA1-939, Inequalities for sums, series and integrals, Mathematics

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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