The function $(b^x-a^x)/x$: Logarithmic convexity and applications to extended mean values

Details The function $(b^x-a^x)/x$: Logarithmic convexity and applications to extended mean values The function $(b^x-a^x)/x$: Logarithmic convexity and applications to extended mean values

2009-03-06

arxiv.org/abs/0903.1203v2

Bai-Ni Guo and Feng Qi, The function $(b^x-a^x)/x$: Logarithmic convexity and applications to extended mean values, Filomat 25

Mathematics

Classical Analysis and ODEs

8 pages

Scientific paper

10.2298/FIL1104063G

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.

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