Mathematica Eterna
Open Access

Abstract

Optimal Convex Combination Bounds for The Square Root Mean

Meng Xiangju and GAO Hongya

The optimal value of parameters α and β are obtained to make the following double inequality holds for all a, b > 0 with a 6= b , αA(a, b) + (1 − a)C(a, b) < Q(a, b) < βA(a, b) + (1 − β)C(a, b) where A(a,b), C(a,b) and Q(a,b) denote arithmetic mean,the ontraharmonic mean,the square root mean of two different positive numbers a and b respectively.