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A Best Possible Double Inequality for Power Mean

descriptionPublicationkeyboard_double_arrow_right Article , Other literature type 01 Jan 2012Publisher:WileyJournal:Journal of Applied Mathematics, volume 2,012 (issn: 1110-757X, eissn: 1687-0042, Copyright policy )
Authors: Li, Yong-Min; Long, Bo-Yong; Chu, Yu-Ming;

doi: 10.1155/2012/379785

A Best Possible Double Inequality for Power Mean

Abstract

We answer the question: for any p, q ∈ ℝ with p ≠ q and p ≠ −q, what are the greatest value λ = λ(p, q) and the least value μ = μ(p, q), such that the double inequality holds for all a, b > 0 with a ≠ b? Where Mp(a, b) is the pth power mean of two positive numbers a and b.

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Keywords

QA1-939, Mathematics

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citations
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!
2
Average
Average
Average
gold