Abstract
As a generalization of a result proved independently by Kurepa and Jurkat on additive functions on \({\mathbb R}\) satisfying certain functional equations, we determine multiadditive functions on \({\mathbb R}^n\) with a positive integer n greater than 1 satisfying certain functional equations similar to those considered in the one variable case.
Similar content being viewed by others
References
Grza̧ślewicz, A.: Some remarks to additive functions. Math. Jpn. 23 (1978/79), 573–578
Grza̧ślewicz, A.: On the solution of the system of functional equations related to quadratic functionals. Glas. Mat. Ser. III 14(34), 77–82 (1979)
Halperin, I.: Problem 448. Colloq. Math. 11, 140 (1963)
Jurkat, W.B.: On Cauchy’s functional equation. Proc. Am. Math. Soc. 16, 683–686 (1965)
Kannappan, Pl, Kurepa, S.: Some relations between additive functions I. Aequationes Math. 4, 163–175 (1970)
Kannappan, Pl, Kurepa, S.: Some relations between additive functions II. Aequationes Math. 6, 46–58 (1971)
Kuczma, M.: An Introduction to the Theory of Functional Equations and Inequalities, Cauchy’s Equation and Jensen’s Inequality, 2nd edn. Birkhäuser Verlag, Basel (2009)
Kurepa, S.: The Cauchy functional equation and the scalar product in vector spaces. Glasnik Mat.-Fiz. Astronom. Ser. II Društvo Mat. Fiz. Hrvatske 19, 23–36 (1964)
Kurepa, S.: Remarks on the Cauchy functional equation. Publ. Inst. Math. (Beograd) (N.S.) 5(19), 85–88 (1965)
Nishiyama, A., Horinouchi, S.: On a system of functional equations. Aequationes Math. 1, 1–5 (1968)
Acknowledgements
The author would like to thank the anonymous referee for the careful reading of the manuscript, and especially for the valuable comments that made it possible to mention, after the Example in the introduction, further problems generalizing the main result of this paper.
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Amou, M. Multiadditive functions satisfying certain functional equations. Aequat. Math. 93, 345–350 (2019). https://doi.org/10.1007/s00010-018-0627-7
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-018-0627-7