English

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 bxaxx\frac{b^x-a^x}x, where x0x\ne0 and b>a>0b>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.

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

R2 v1 2026-06-21T12:19:07.194Z