OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR THE GEOMETRIC COMBINATION OF ARITHMETIC AND HARMONIC MEANS

Bo-Yong Long

doi:10.22342/jims.17.2.5.85-95

Bo-Yong Long ⁽¹⁾

(1) College of Mathematics Science, Anhui University, China

https://doi.org/10.22342/jims.17.2.5.85-95

Issue
Volume 17 Number 2 (October 2011)

Submitted
December 31, 2011

Accepted
December 31, 2011

Published
December 31, 2011

Keywords:

Generalized logarithmic mean, arithmetic mean, harmonic mean

Abstract Full Paper

Abstract

In this paper, we answer the question: for 2 (0; 1), what are thegreatest value p = p() and least value q = q(), such that the double inequalityLp(a; b) A(a; b)H1􀀀(a; b) Lq(a; b) holds for all a; b > 0? where Lp(a; b),A(a; b), and H(a; b) are the p-th generalized logarithmic, arithmetic, and harmonicmeans of a and b, respectively.

DOI : http://dx.doi.org/10.22342/jims.17.2.5.85-95

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Authors

Bo-Yong Long

College of Mathematics Science, Anhui University

lbymxy@q163.com (Primary Contact)

Long, B.-Y. (2011). OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR THE GEOMETRIC COMBINATION OF ARITHMETIC AND HARMONIC MEANS. Journal of the Indonesian Mathematical Society, 17(2), 85–95. https://doi.org/10.22342/jims.17.2.5.85-95