Optimal Lower Generalized Logarithmic Mean Bound for the Seiffert Mean

Abstract

We present the greatest value $p$ such that the inequality $P(a,b)>L_p(a,b)$ holds for all $a,b>0$ with $a\ne b$, where $P(a,b)$ and $L_p(a,b)$ denote the Seiffert and $p$th generalized logarithmic means of $a$ and $b$, respectively.