Optimal lower power mean bound for the convex combination of harmonic and logarithmic means (Q554909)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Optimal lower power mean bound for the convex combination of harmonic and logarithmic means |
scientific article; zbMATH DE number 5930754
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Optimal lower power mean bound for the convex combination of harmonic and logarithmic means |
scientific article; zbMATH DE number 5930754 |
Statements
Optimal lower power mean bound for the convex combination of harmonic and logarithmic means (English)
0 references
22 July 2011
0 references
Summary: We find the least value \(\lambda \in (0, 1)\) and the greatest value \(p = p(\alpha)\) such that \(\alpha H(a, b) + (1 - \alpha)L(a, b) > M_p (a, b)\) for \(\alpha \in [\lambda, 1)\) and all \(a, b > 0\) with \(a \neq b\), where \(H(a, b)\), \(L(a, b)\), and \(M_p(a, b)\) are the harmonic, logarithmic, and \(p\)-th power means of two positive numbers \(a\) and \(b\), respectively.
0 references
