Optimal bounds for Neuman-Sándor mean in terms of one-parameter centroidal mean

摘要

In the paper, we find the best possible parameters $lpha,eta in ({0,1})$ and $lambda, mu in ({1/2,1})$ such that the double inequalities $sqrt{lpha E^{2}( {a,b})+(1-lpha)A^{2}({a,b})}0$ with $ae b$, here $NS(a,b) = ({a-b}) / [2sin{h^{-1}}$ $(({a-b})/({a+b}))]$, $A(a,b)=({a+b})/2$ and $E(a,b)=2({a^{2}+ab+b^{2}})/[{3({a+b})}]$ are Neuman-S'{a}ndor, arithmetic and centroidal means of two positive real numbers $a$ and $b$, respectively.