Abstract
We determine continuous solutions of the Goła̧b–Schinzel functional equation on cylinders.
Article PDF
Similar content being viewed by others
References
Aczél, J., Dhombres, J.: Functional Equations in Several Variables. Encyclopedia of Mathematics and Its Applications, vol. 31. Cambridge University Press, Cambridge (1989)
Aczél, J., Schwaiger, J.: Continuous solutions of the Goła̧b–Schinzel equation on the nonnegative reals and on related domains. Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II(208), 171–177 (1999)
Bahyrycz, A., Brzdȩk, J.: On solutions of the d’Alembert equation on a restricted domain. Aequ. Math. 85, 169–183 (2013)
Brzdȩk, J.: On continuous solutions of a conditional Goła̧b–Schinzel equation. Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 138, 3–6 (2001)
Brzdȩk, J.: The Goła̧b–Schinzel equation and its generalizations. Aequ. Math. 70, 14–24 (2005)
Brzdȩk, J., Mureńko, A.: On a conditional Goła̧b–Schinzel equation. Arch. Math. 85, 503–511 (2005)
Chudziak, J., Kočan, Z.: Continuous solutions of conditional composite type functional equations. Results Math. 66, 199–211 (2014)
Chudziak, J., Kočan, Z.: Functional equations of the Goła̧b–Schinzel type on a cone. Monast. Math. 178, 521–537 (2015)
Dhombres, J., Ger, R.: Equations de Cauchy conditionnelles. C. R. Acad. Sci. Paris Ser. A 280, 513–515 (1975)
Dhombres, J., Ger, R.: Conditional Cauchy equations. Glas. Matem. 13, 39–62 (1978)
Kahlig, P., Matkowski, J.: A modified Goła̧b–Schinzel equation on restricted domain (with applications to meteorology and fluid mechanics). Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II(211), 117–136 (2002)
Kahlig, P., Matkowski, J.: The Goła̧b–Schinzel functional equation restricted to half-lines. Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II(212), 57–67 (2003)
Kuczma, M.: An Introduction to the Theory of Functional Equations and Inequalities, 2nd edn. Birkhäuser, Berlin (2009)
Matkowski, J.: On a system of symultaneous iterative functional equations. Ann. Math. Siles 9, 123–135 (1995)
Mureńko, A.: On solutions of a conditional generalization of the Goła̧b–Schinzel equation. Publ. Math. Debr. 63, 693–702 (2003)
Nabeya, S.: On the functional equation \(f(p+qx+rf(x))=a+bx+cf(x)\). Aequ. Math. 11, 199–211 (1974)
Reich, L.: Über die stetigen Lösungen der Goła̧b–Schinzel–Gleichung auf \(\mathbb{R}\) und auf \(\mathbb{R}_{\ge 0}\). Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II(208), 165–170 (1999)
Reich, L.: Über die stetigen Lösungen der Goła̧b–Schinzel–Gleichung auf \(\mathbb{R}_{\ge 0}\). Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 138, 7–12 (2001)
Sablik, M.: A conditional Goła̧b–Schinzel equation. Anz. Österreich. Akad. Wiss. Math.-Natur. Kl. 137, 11–15 (2000)
Salzmann, H., Grundhöfer, T., Hähl, H., Löven, R.: The Classical Fields: Structural Features of the Real and Rational Numbers. Encyclopedia of Mathematics and its Applications. Cambridge University Press, Cambridge (2007)
Acknowledgements
The research was supported, in part, by RVO funding for IČ47813059.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.
About this article
Cite this article
Chudziak, J., Kočan, Z. Goła̧b–Schinzel equation on cylinders. Aequat. Math. 91, 547–561 (2017). https://doi.org/10.1007/s00010-017-0475-x
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-017-0475-x