On harmonic representation of means
Classical Analysis and ODEs
2013-10-14 v1
Abstract
We characterize continuous, symmetric and homogeneous means that can be represented in the form \begin{equation*} \frac{1}{M(x,y)}=\int_0^1 \frac{dt}{N\left(\tfrac{x+y}{2}-t\tfrac{x-y}{2},\tfrac{x+y}{2}+t\tfrac{x-y}{2}\right)}. \end{equation*} New inequalities for means are derived from such representation.
Keywords
Cite
@article{arxiv.1310.3063,
title = {On harmonic representation of means},
author = {Alfred Witkowski},
journal= {arXiv preprint arXiv:1310.3063},
year = {2013}
}