Let $r$ be a real number. The generalized logarithmic mean $L_{r}(a,b)$ and Seiffert mean $P(a,b)$ of the positive real numbers $a$ and $b$ are defined by $$ L_{r}(a,b)=\cases a, & a=b,\\\left(\dfrac{b^{r}-a^{r}}{r(b-a)}\right)^{1/(r-1)},& r\neq 1,\ r\neq 0,\ a\neq b,\\\dfrac{1}{e}\left( \dfrac{b^{a}}{a^{a}}\right)^{1/(b-a)},& r= 1,\ a\neq b,\\\dfrac{b-a}{\log b-\log a}, & r= 0,\ a\neq b, \endcases $$ and for $a\neq b$ $$ P(a,b)= \frac{a-b}{4 \arctan(\sqrt{a/b}-\pi)}, $$ respectively. \par The authors of the paper under review find the greatest value $\alpha$ and the least value $\beta$ such that the inequalities $$ L_{\alpha}(a,b)< P(a,b)\quad\text{and}\quad P(a,b)< L_{\beta}(a,b), $$ respectively, hold for all positive $a,b$ with $a\neq b$.