The function $(b^x-a^x)/x$: Logarithmic convexity and applications to extended mean values
Classical Analysis and ODEs
2011-07-19 v2
Abstract
In the present paper, we first prove the logarithmic convexity of the elementary function , where and . 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.
Keywords
Cite
@article{arxiv.0903.1203,
title = {The function $(b^x-a^x)/x$: Logarithmic convexity and applications to extended mean values},
author = {Feng Qi and Bai-Ni Guo},
journal= {arXiv preprint arXiv:0903.1203},
year = {2011}
}
Comments
8 pages