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- W4289490621 abstract "Let $Isubset (0,infty )$ 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,yright) =left( fcirc gright) ^{-1}left( fleft( xright) cdot gleft( yright) 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." @default.
- W4289490621 created "2022-08-02" @default.
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- W4289490621 date "2018-09-26" @default.
- W4289490621 modified "2023-09-29" @default.
- W4289490621 title "Invariance in a class of operations related to weighted quasi-geometric means" @default.
- W4289490621 doi "https://doi.org/10.48550/arxiv.1809.10675" @default.
- W4289490621 hasPublicationYear "2018" @default.
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