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Our aim is to study continuous solutions φ of the classical linear iterative equation
φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y),
where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.
φ(f(x,y)) = g(x,y)φ(x,y) + h(x,y),
where the given function f is defined as a pair of means. We are interested in the case when f has no fixed points. In turns out that in such a case continuous solutions of (1) depend on an arbitrary function.
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
27-46
Opis fizyczny
Daty
wydano
2005
otrzymano
2004-06-10
Twórcy
autor
- Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra, Prof. Z. Szafrana 4a, 65-516 Zielona Góra, Poland
Bibliografia
- [1] M. Kuczma, Functional equations in a single variable, Monografie Mat. 46, Polish Scientific Publishers, Warszawa 1968.
- [2] J. Matkowski, Invariant and complementary quasi-arithmetic means, Aequationes Math. 57 (1999), 87-107.
- [3] J. Matkowski, Iterations of mean-type mappings and invariant means, Ann. Math. Sil. 13 (1999), 211-226.
- [4] K. Sajbura, Level sets of continuous functions increasing with respect to each variable, Discuss. Math. DICO 25 (2005), 19-26.
Typ dokumentu
Bibliografia
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Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmdico_1057