Reference : Invariance in a class of operations related to weighted quasi-geometric means
 Document type : Scientific journals : Article Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics Focus Areas : Computational Sciences To cite this reference: http://hdl.handle.net/10993/36748
 Title : Invariance in a class of operations related to weighted quasi-geometric means Language : English Author, co-author : Devillet, Jimmy [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >] Matkowski, Janusz [] Publication date : In press Journal title : Fuzzy Sets and Systems Publisher : Elsevier Peer reviewed : Yes (verified by ORBilu) Audience : International ISSN : 0165-0114 City : Amsterdam Country : Netherlands Keywords : [en] 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. Funders : University of Luxembourg - UL ; Fonds National de la Recherche - FnR Target : Researchers ; Professionals ; Students Permalink : http://hdl.handle.net/10993/36748 DOI : 10.1016/j.fss.2020.08.019 FnR project : FnR ; FNR10949314 > Gabor Wiese > GSM > Geometric and Stochastic Methods in Mathematics and Applications > 01/10/2016 > 31/03/2023 > 2016

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