OPTIMAL GENERALIZED LOGARITHMIC MEAN BOUNDS FOR THE GEOMETRIC COMBINATION OF ARITHMETIC AND HARMONIC MEANS
Abstract: In this paper, we
answer the question: for α 2 (0; 1), what are the greatest value p = p(α) and
least value q = q(α), such that the double inequality L p(a; b) ≤ Aα(a;
b)H1−α(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.
Author: Bo-Yong Long and
Yu-Ming Chu
Journal Code: jpmatematikagg110014
