Geodesic
Invariance in the class of weighted quasi-arithmetic means
Justyna Jarczyk1 ; Janusz Matkowski2
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
Annales Polonici Mathematici, Tome 88 (2006) no. 1, pp. 39-51

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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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