Continuity of Lebesgue measurable solutions of a generalized Gołąb-Schinzel equation

• Autorzy: Jabłońska E.
• Języki publikacji: EN

Abstrakty

EN

Let k, n be positive integers and let f : Rn -> R be a solution of the functional equation f(x + f(x)ky)=f(x)f(y). We prove that, if there is a real positive a such that the set [x is an element of Rn : |f(x)| is an element of (0,a)} contains a subset of positive Lebesgue measure, then f is continuous. As a consequence of this we obtain that every Lebesgue measurable solution f : Rn -> R of the equation is continuous or equal zero almost everywhere (i.e. there is a set A C R of the Lebesgue measure zero with f(Rn \ A) = {0}).

Słowa kluczowe

EN

Gołąb-Schinzel equation; Lebesgue solutions; supergroups

PL

równania Gołąb-Schinzel; rozwiązania Lebesgue; podgrupy

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 1
• Strony: 91--96
• Opis fizyczny: Bibliogr. 10 poz.

Twórcy

autor

Jabłońska E.

• Department of Mathematics Technical University of Rzeszów W. Pola 2, 35-959 Rzeszów, Poland,

Bibliografia

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