Optimal bounds for a Gaussian Arithmetic-Geometric type mean by quadratic and contraharmonic means

Junxuan Shen

In this paper, we present the best possible parameters ${\alpha }_i,{\beta }_i(i=1,2,3)$ and ${\alpha }_4,{\beta }_4\in (1/2,1)$ such that the double inequalities \begin{align*} α_1Q(a,b)+(1-α_1)C(a,b)&<AG_{Q…