Optimal Bounds for Seiffert Mean in terms of One-Parameter Means

Abstract

The authors present the greatest value $r_1$ and the least value $r_2$ such that the double inequality holds for all $a\text{,\hspace{0.17em}}b>0$ with $a\ne b$, where $T(a\text{,\hspace{0.17em}}b)$ and $J_p(a\text{,\hspace{0.17em}}b)$ denote the Seiffert and pth one-parameter means of two positive numbers a and b, respectively.