Geodesic
Invariance in the class of weighted quasi-arithmetic means
Justyna Jarczyk1 ; Janusz Matkowski2
1Faculty of Mathematics Computer Science and Econometrics University of Zielona Góra Szafrana 4a 65-516 Zielona Góra, Poland
2Faculty of Mathematics Computer Science and Econometrics University of Zielona Góra Szafrana 4a 65-516 Zielona Góra, Poland and Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland
Annales Polonici Mathematici, Tome 88 (2006) no. 1, pp. 39-51
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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Under the assumption of twice continuous differentiability of some of the functions involved we determine all the weighted quasi-arithmetic means $M,N,K$ such that $K$ is $(M,N)$-invariant, that is, $K\circ (M,N)=K.$ Some applications to iteration theory and functional equations are presented.
DOI : 10.4064/ap88-1-3
Keywords: under assumption twice continuous differentiability functions involved determine weighted quasi arithmetic means invariant circ applications iteration theory functional equations presented

Justyna Jarczyk  1   ; Janusz Matkowski  2

1 Faculty of Mathematics Computer Science and Econometrics University of Zielona Góra Szafrana 4a 65-516 Zielona Góra, Poland
2 Faculty of Mathematics Computer Science and Econometrics University of Zielona Góra Szafrana 4a 65-516 Zielona Góra, Poland and Institute of Mathematics Silesian University Bankowa 14 40-007 Katowice, Poland 
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Justyna Jarczyk; Janusz Matkowski. Invariance in the class of weighted quasi-arithmetic means. Annales Polonici Mathematici, Tome 88 (2006) no. 1, pp. 39-51. doi: 10.4064/ap88-1-3

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