OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR THE GEOMETRIC COMBINATION OF ARITHMETIC AND HARMONIC MEANS - Long, Bo-Yong (Journal of the Indonesian Mathematical Society, 2011)
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)H1ô€€€(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 :Â http://dx.doi.org/10.22342/jims.17.2.5.85-95