Reference : Invariance in a class of operations related to weighted quasi-geometric means
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Physical, chemical, mathematical & earth Sciences : Mathematics
http://hdl.handle.net/10993/36748
Invariance in a class of operations related to weighted quasi-geometric means
English
Devillet, Jimmy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Matkowski, Janusz []
29-Sep-2018
No
[en] invariant functions ; mean ; invariant mean ; reflexivity ; iteration ; functional equation
[en] Let $I\subset (0,\infty )$ be an interval that is closed with respect to the
multiplication. The operations $C_{f,g}\colon I^{2}\rightarrow I$ of the
form
\begin{equation*}
C_{f,g}\left( x,y\right) =\left( f\circ g\right) ^{-1}\left( f\left(
x\right) \cdot g\left( y\right) \right) \text{,}
\end{equation*}
where $f,g$ are bijections of $I$ are considered. Their connections with
generalized weighted quasi-geometric means is presented. It is shown that invariance\
question within the class of this operations leads to means of iterative
type and to a problem on a composite functional equation. An application of
the invariance identity to determine effectively the limit of the sequence
of iterates of some generalized quasi-geometric mean-type mapping, and the
form of all continuous functions which are invariant with respect to this
mapping are given. The equality of two considered operations is also discussed.
University of Luxembourg - UL ; Fonds National de la Recherche - FnR
Researchers
http://hdl.handle.net/10993/36748

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