The function $(b^x-a^x)/x$: Logarithmic convexity and applications to extended mean values
arXiv:0903.1203 · doi:10.2298/FIL1104063G
Abstract
In the present paper, we first prove the logarithmic convexity of the elementary function $\frac{b^x-a^x}x$, where $x\ne0$ and $b>a>0$. Basing on this, we then provide a simple proof for Schur-convex properties of the extended mean values, and, finally, discover some convexity related to the extended mean values.
8 pages