Reference : Invariance in a class of operations related to weighted quasi-geometric means
 Document type : E-prints/Working papers : First made available on ORBilu Discipline(s) : Physical, chemical, mathematical & earth Sciences : Mathematics 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 : 29-Sep-2018 Peer reviewed : No 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 Permalink : http://hdl.handle.net/10993/36748

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Open access
InvQGM.pdfAuthor preprint346.41 kBView/Open

All documents in ORBilu are protected by a user license.