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

Bo-Yong Long

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


Keywords


Generalized logarithmic mean, arithmetic mean, harmonic mean

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Abstract Full Paper


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

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Journal of the Indonesian Mathematical Society
Mathematics Department, Universitas Gadjah Mada
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p-ISSN: 2086-8952 | e-ISSN: 2460-0245


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