Level sets of continuous functions increasing with respect to each variable

• Autorzy: Katarzyna Sajbura
• Języki publikacji: EN

Abstrakty

EN

We are going to prove that level sets of continuous functions increasing with respect to each variable are arcwise connected (Theorem 3) and characterize those of them which are arcs (Theorem 2). In [3], we will apply the second result to the classical linear functional equation
φ∘f = gφ + h
(cf., for instance, [1] and [2]) in a case not studied yet, where f is given as a pair of means, that is so-called mean-type mapping.

Słowa kluczowe

EN

level set; continuous function; function increasing with respect to each variable; arcwise connectedness

Kategorie tematyczne

• 26B35: Special properties of functions of several variables, H\"older conditions, etc.
• 54C50: Special sets defined by functions

• 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: 19-26

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] M. Kuczma, B. Choczewski and R. Ger, Iterative functional equations, Encyclopedia of mathematics and its applications 32, Cambridge University Press, Cambridge, 1990.
• [3] K. Sajbura, On a linear functional equation with a mean-type mapping having no fixed points, Discuss. Math. DICO 25 (2005), 27-46.

Identyfikatory

DOI

10.7151/dmgt.1056