Abstract
It is known that some problems in meteorology and fluid dynamics lead to Goła̧b–Schinzel type equations on a restricted domain. Inspired by a question of Professor L. Reich we determine the solutions of conditional composite type functional equations related to the Goła̧b–Schinzel equation.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Aczél, J., Dhombres, J.: Functional equations in several variables. In: Encyclopedia of Mathematics and its Applications, vol. 31. Cambridge University Press, Cambridge (1989)
Aczél J., Goła̧b S.: Remarks on one-parameter subsemigroups of the affine group and their homo- and isomorphisms. Aequationes Math. 4, 1–10 (1970)
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)
Aichinger E., Farag M.: On when the multiplicative center of a near-ring is a subnear-ring. Aequationes Math. 48, 46–59 (2004)
Brillouët-Belluot N., Brzdȩk J.: On continuous solutions and stability of a conditional Goła̧b–Schinzel equation. Publ. Math. Debrecen 72, 441–450 (2008)
Brillouët-Belluot N., Brzdȩk J., Chudziak J.: On continuous solutions of a class of conditional equations. Publ. Math. Debrecen 75, 11–22 (2009)
Brillouët N., Dhombres J.: Équations fonctionnelles et recherche de sous-groupes. Aequationes Math. 31, 253–293 (1986)
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. Aequationes Math. 70, 14–24 (2005)
Brzdȩk J., Mureńko A.: On a conditional Goła̧b–Schinzel equation. Arch. Math. (Basel) 85, 503–511 (2005)
Chudziak J.: Semigroup-valued solutions of the Goła̧b–Schinzel type functional equation. Abh. Math. Sem. Univ. Hamburg 76, 91–98 (2006)
Chudziak J.: Associative solutions of a composite generalization of addition formulae. Acta Math. Hungar. 117, 141–152 (2007)
Goła̧b S., Schinzel A.: Sur l’équation fonctionnelle f(x + yf(x)) = f(x)f(y). Publ. Math. Debrecen 6, 113–125 (1959)
Ilse D., Lehmann I., Schulz W.: Gruppoide und Funktionalgleichungen. VEB Deutscher Verlag der Wissenschaften, Berlin (1984)
Jabłońska E.: Continuous on rays solutions of an equation of the Goła̧b–Schinzel type. J. Math. Anal. Appl. 375, 223–229 (2011)
Jabłońska E.: On continuous solutions of an equation of the Goła̧b–Schinzel type. Bull. Aust. Math. Soc. 87, 10–17 (2013)
Jabłońska, E.: On locally bounded above solutions of an equation of the Goła̧b–Schinzel type. Aequationes Math. doi:10.1007/s00010-013-0195-9
Kahlig P., Matkowski J.: A modified Goła̧b-Schinzel equation on a restricted domain (with applications to meteorology and fluid mechanics). Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II. 211, 117–136 (2002)
Kuczma, M.: An Introduction to the Theory of Functional Equations and Inequalities, Państwowe Wydawnictwo Naukowe, Uniwersytet Śla̧ski, Warszawa-Kraków-Katowice (1985)
Luneburg H., Plaumann P.: Die Funktionalgleichung von Goła̧b und Schinzel in Galoisfeldern. Arch. Math. (Basel) 28, 55–59 (1977)
Mureńko A.: On solutions of the Goła̧b–Schinzel equation. Int. J. Math. Math. Sci. 27, 541–546 (2001)
Mureńko A.: On solutions of a conditional generalization of the Goła̧b–Schinzel equation. Publ. Math. Debrecen 63, 693–702 (2003)
Plaumann P., Strambach S.: Zweidimensionale Quasialgebren mit Nullteilern. Aequationes Math. 15, 249–264 (1977)
Reich L.: Über die stetigen Lösungen der Goła̧b–Schinzel-Gleichung auf \({\mathbb{R}}\) und auf \({\mathbb{R}_{\geq 0}}\), Österr. Akad. Wiss. Math.-Natur. Kl. Sitzungsber. II. 208, 165–170 (1999)
Reich L.: Über die stetigen Lösungen der Goła̧b–Schinzel-Gleichung auf \({\mathbb{R}_{\geq 0}}\), 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)
Sobek B.: Pexider equation on a restricted domain. Demonstratio Math. 43, 81–88 (2010)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Open Access This article is distributed under the terms of the Creative Commons Attribution License which permits any use, distribution, and reproduction in any medium, provided the original author(s) and the source are credited.
About this article
Cite this article
Chudziak, J., Kočan, Z. Continuous Solutions of Conditional Composite Type Functional Equations. Results. Math. 66, 199–211 (2014). https://doi.org/10.1007/s00025-014-0372-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00025-014-0372-8