Abstract
Let (S, +) be a (semi)group and let (R,+, ·) be an integral domain. We study the solutions of a Pexider type functional equation
for functions f and g mapping S into R. Our chief concern is to examine whether or not this functional equation is equivalent to the system of two Cauchy equations
for every \({x,y \in S}\).
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aczél J.: Lectures on Functional Equations and Their Applications. Academic Press, New York (1966)
Aczél J., Dhombres J.: Functional Equations in Several Variables. Cambridge University Press, Cambridge (1989)
Dhombres J.: Relations de dépendance entre équations fonctionnelles de Cauchy. Aequationes Math. 35, 186–212 (1988)
Ger R.: On an equation of ring homomorphisms. Publ. Math. Debrecen 52, 397–417 (1998)
Ger R.: Ring homomorphisms equation revisited. Rocznik Nauk.-Dydakt. Prace Mat. 17, 101–115 (2000)
Ger R., Reich L.: A generalized ring homomorphisms equation. Monatsh. Math. 159, 225–233 (2010)
Kuczma, M.: An Introduction to the Theory of Functional Equations and Inequalities. Polish Scientific Publishers and Silesian University Press, Warszawa-Kraków-Katowice (1985)
Author information
Authors and Affiliations
Corresponding author
Additional information
Dedicated to Professor János Aczél on his 85th birthday
Rights and permissions
About this article
Cite this article
Ger, R. Additivity and exponentiality are alien to each other. Aequat. Math. 80, 111–118 (2010). https://doi.org/10.1007/s00010-010-0012-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-010-0012-7