On a linear functional equation with a mean-type mapping having no fixed points

• Autorzy: Katarzyna Sajbura
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

linear functional equation; iteration; mean; continuous solution; solution depending on an arbitrary function

Kategorie tematyczne

• 39B12: Iteration theory, iterative and composite equations
• 26E60: Means

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae, Differential Inclusions, Control and Optimization
• Rocznik: 2005
• Tom: 25
• Numer: 1
• Strony: 27-46

Daty

wydano

2005

otrzymano

2004-06-10

Twórcy

autor

Katarzyna Sajbura

• 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.

Identyfikatory

DOI

10.7151/dmgt.1057