Reference : Invariance in a class of operations related to weighted quasi-geometric means
E-prints/Working papers : First made available on ORBilu
Physical, chemical, mathematical & earth Sciences : Mathematics
Invariance in a class of operations related to weighted quasi-geometric means
Devillet, Jimmy mailto [University of Luxembourg > Faculty of Science, Technology and Communication (FSTC) > Mathematics Research Unit >]
Matkowski, Janusz []
[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
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{,}
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

File(s) associated to this reference

Fulltext file(s):

Open access
InvQGM.pdfAuthor preprint346.41 kBView/Open

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.