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, Volume 88 (2006) no. 1, pp. 39-51

See the original article notice from the Institute of Mathematics Polish Academy of Sciences source

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 
Justyna Jarczyk; Janusz Matkowski. Invariance in the class of weighted quasi-arithmetic means. Annales Polonici Mathematici, Volume 88 (2006) no. 1, pp. 39-51. doi: 10.4064/ap88-1-3
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