Year: 2021
Type: preprint
Abstract: It is observed that in some money exchange operations, the applied $n$ -variable mean $M$ should be self reciprocally-conjugate, i.e. it should satisfy the equality \[ M\left( x_{1},\ldots,x_{n}\right) M\left( \frac{1}{x_{1}},\ldots,\frac{1}{x_{n}} \right) =1,\quad x_{1},\ldots,x_{n}>0. \] The main result says that the only weighted quasiarithmetic mean satisfying this condition is the weighet geometric mean.
Source: arXiv (Cornell University)
Authors: Bojarski, Jacek, Matkowski, Janusz
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4295676962