Optimal Generalized Logarithmic Mean Bounds for the Geometric Combination of Arithmetic and Harmonic Means

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.17.2.5.85-9