Bo-Yong Long
College of Mathematics Science, Anhui University

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OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR THE GEOMETRIC COMBINATION OF ARITHMETIC AND HARMONIC MEANS Long, Bo-Yong
Journal of the Indonesian Mathematical Society Volume 17 Number 2 (October 2011)
Publisher : IndoMS

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.22342/jims.17.2.5.85-95

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