Cauchy type functional equations related to some associative rational functions

Authors

  • Katarzyna Domańska Jan Długosz University in Częstochowa, Faculty Science and Technology

Keywords:

functional equation, rational function, associativity

Abstract

L. Losonczi [4] determined local solutions of the generalized Cauchy equation f(F(x, y))= f(x) + f(y) on components of the denition of a given associative rational function F. The class of the associative rational function was described by A. Chéritat [1] and his work was followed by paper [3] of the author. The aim of the present paper is to describe local solutions of the equation considered for some singular associative rational functions.

References

Chéritat, Arnaud. "Fractions rationnelles associatives et corps quadratiques." Revue des Mathématiques de l’Enseignement Supérieur 109 (1998-1999): 1025-1040.
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Daróczy, Zoltán and László Losonczi. "Über die Erweiterung der auf einer Punktmenge additiven Funktionen." Publ. Math. Debrecen 14 (1967): 239-245.
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Domańska, Katarzyna. "An analytic description of the class of rational associative functions." Ann. Univ. Paedagog. Crac. Stud. Math. 11 (2012): 111-122.
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Losonczi, László. "Local solutions of functional equations." Glas. Mat. Ser. III 25(45), no. 1 (1990): 57-67.
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Published

2019-07-29

How to Cite

Domańska, K. (2019). Cauchy type functional equations related to some associative rational functions. Annales Universitatis Paedagogicae Cracoviensis Studia Mathematica, 18, 145–156. Retrieved from https://studmath.up.krakow.pl/article/view/7950

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