Author/Authors :
Chu, Yu-Ming Hunan City University - School of Mathematics and Computation Sciences, China , Shi, Ming-Yu Heibei University - College of Mathematics and Computer Science, China , Jiang, Yue-Ping Hunan University - School of Mathematics and Econometrics, China
Abstract :
For all a, b 0, the following two optimal inequalities are presented: H^α(a, b)L^1-α(a, b) ≥ M1-4α/ 3(a, b) for α element of [ 1/ 4, 1), and H^α(a, b)L^1-α(a, b) ≤ M1-4α/ 3 (a, b) for α element of (0, 3 √5-5/ 40 ]. Here, H(a, b), L (a, b), and Mp (a, b) denote the harmonic, logarithmic, and power means of order p of two positive numbers a and b, respectively.
