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Warianty tytułu
Języki publikacji
Abstrakty
We deal with a functional equation of the form ƒ(x + y) = F(ƒ(x), ƒ(y)) (so called addition formula) assuming that the given binary operation F is associative but its domain is not connected. The aim of the present paper is to discuss solutions of the equation [formula]. It turns out that this functional equation characterized an inverse proportionality type function, but if the domain of the unknown function has no neutral element. In this paper we admit fairly general structure in the domain of the unknown function.
Rocznik
Tom
Strony
175--178
Opis fizyczny
Bibliogr. 5 poz.
Twórcy
autor
- Jan Długosz University, Institute of Mathematics and Computer Science, 42-200 Częstochowa, Al. Armii Krajowej 13/15, Poland
Bibliografia
- [1] A. Chéritat, Fractions rationnelles associatives et corps quadratiques, Revue des Mathématiques de l’Enseignement Supérieur 109 (1998-1999), 1025-1040.
- [2] K. Domańska, An analytic description of the class of rational associative functions, Annales Universitatis Pedagogicae Cracoviensis, Studia Mathematica XI (2012), 111-122.
- [3] K. Domańska, On some addition formulas for homographic type functions, Scientific Issues, Jan Długosz University in Czestochowa, Mathematics XVII (2012), 17-24.
- [4] J. G. Dhombres, R. Ger, Équations de Cauchy conditionelles, Comptes Rendus Academic Scientific Paris 280 (1975), 513-515.
- [5] R. Ger, On some functional equations with a restricted domain, II, Fund. Math. 98 (1978), 249-272.
Typ dokumentu
Bibliografia
Identyfikator YADDA
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