Article (Scientific journals)
Invariance in a class of operations related to weighted quasi-geometric means
DEVILLET, Jimmy; Matkowski, Janusz
In pressIn Fuzzy Sets and Systems
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Keywords :
invariant functions; mean; invariant mean; reflexivity; iteration; functional equation
Abstract :
[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.
Disciplines :
Mathematics
Author, co-author :
DEVILLET, Jimmy ;  University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit
Matkowski, Janusz
External co-authors :
yes
Language :
English
Title :
Invariance in a class of operations related to weighted quasi-geometric means
Publication date :
In press
Journal title :
Fuzzy Sets and Systems
ISSN :
0165-0114
eISSN :
1872-6801
Publisher :
Elsevier, Amsterdam, Netherlands
Peer reviewed :
Peer Reviewed verified by ORBi
Focus Area :
Computational Sciences
FnR Project :
FNR10949314 - Geometric And Stochastic Methods In Mathematics And Applications, 2015 (01/10/2016-31/03/2023) - Gabor Wiese
Funders :
University of Luxembourg - UL
FNR - Fonds National de la Recherche
Available on ORBilu :
since 29 September 2018

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