The Optimal Upper and Lower Power Mean Bounds for a Convex Combination of the Arithmetic and Logarithmic Means

Wei-Feng Xia, Yu-Ming Chu and Gen-Di Wang

Abstract and Applied Analysis, 2010, vol. 2010, issue 1

Abstract: For p ∈ ℝ, the power mean Mp(a, b) of order p, logarithmic mean L(a, b), and arithmetic mean A(a, b) of two positive real values a and b are defined by Mp(a, b) = ((ap + bp)/2) 1/p, for p ≠ 0 and Mp(a,b)=ab, for p = 0, L(a, b) = (b − a)/(log b − log a), for a ≠ b and L(a, b) = a, for a = b and A(a, b) = (a + b)/2, respectively. In this paper, we answer the question: for α ∈ (0,1), what are the greatest value p and the least value q, such that the double inequality Mp(a, b) ≤ αA(a, b)+(1 − α)L(a, b) ≤ Mq(a, b) holds for all a, b > 0?

Date: 2010
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1155/2010/604804

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlaaa:v:2010:y:2010:i:1:n:604804

Access Statistics for this article

More articles in Abstract and Applied Analysis from John Wiley & Sons
Bibliographic data for series maintained by Wiley Content Delivery ().