Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean
Sharp bounds for Neuman means in terms of two-parameter contraharmonic and arithmetic mean
In the article, we prove that $\lambda _{1}=1/2+\sqrt{ [ (\sqrt{2}+ \log (1+\sqrt{2}) )/2 ]^{1/\nu }-1}/2$ , $\mu _{1}=1/2+\sqrt{6 \nu }/(12\nu )$ , $\lambda _{2}=1/2+\sqrt{ [(\pi +2)/4 ] ^{1/\nu }-1}/2$ and $\mu _{2}=1/2+\sqrt{3\nu }/(6\nu )$ are the best possible parameters on the interval $[1/2, 1]$ such that the double inequalities $$\begin{aligned}& …