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 | |||

http://hdl.handle.net/10993/36748 | |||

Invariance in a class of operations related to weighted quasi-geometric means | |

English | |

Devillet, Jimmy [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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