J. Devillet

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20182020

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math.CA2018

Invariance in a class of operations related to weighted quasi-geometric means

Jimmy Devillet, Janusz Matkowski

Let $I \subset (0, \infty)$ be an interval that is closed with respect to the multiplication. The operations $C_{f, g} : I^{2} \to I$ of the form \begin{equation*} C_{f,g}…

math.CA2018

A new invariance identity and means

Jimmy Devillet, Janusz Matkowski

The invariance identity involving three operations $D_{f, g} : X \times X \to X$ of the form \begin{equation*} D_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\lef…