Abstract
Our purpose is to provide an affirmative answer to Moszner’s problem [cf. Moszner (Ann Univ Paed Crac Stud Math XI:69–94, 2012), p. 93] concerning the superstability of the Cauchy equation with squares
in the class of functions mapping an Abelian semigroup into a finite-dimensional normed algebra without divisors of zero.
Article PDF
Similar content being viewed by others
References
Baker J.: The stability of the cosine equation. Proc. Am. Math. Soc. 80, 411–416 (1980)
Batko B.: On the stability of an alternative functional equation. Math. Inequal. Appl. 8(4), 685–691 (2005)
Batko B.: Stability of an alternative functional equation. J. Math. Anal. Appl. 339, 303–311 (2008)
Batko, B.: On approximate solutions of functional equations in vector lattices. Abstr. Appl. Anal. 2014 (2014). Art. ID 547673, 10 pages. doi:10.1155/2014/547673
Batko B., Tabor J.: Stability of an alternative Cauchy equation on a restricted domain. Aequ. Math. 57, 221–232 (1999)
Batko B., Tabor J.: Stability of the generalized alternative Cauchy equation. Abh. Math. Sem. Univ. Hamb. 69, 67–73 (1999)
Dhombres J.G., Ger R.: Conditional Cauchy equations. Glasnik Mat. 13(33), 39–62 (1978)
Ger R.: On a characterization of strictly convex spaces. Atti Accad. Sci. Torino. Cl. Sci. Fis. Mat. Natur. 127, 131–138 (1993)
Jung S.-M.: On solution and stability of functional equation f(x + y)2 = af(x)f(y) + bf(x)2 + cf(y)2. Bull. Korean Math. Soc. 34, 561–571 (1997)
Moszner Z.: On stability of some functional equations and topology of their target spaces. Ann. Univ. Paed. Crac. Stud. Math. XI(122), 69–94 (2012)
Schwaiger, J.: Remark 13. In: Report of Meeting, The 41st International Symposium on Functional Equations Aequationes Mathematics, vol. 67, p. 309 (2004)
Tabor J.: Stability of the Fischer–Muszély functional equation. Publ. Math. Debrecen 62/1-2, 205–211 (2003)
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
Batko, B. Superstability of the Cauchy equation with squares in finite-dimensional normed algebras. Aequat. Math. 89, 785–789 (2015). https://doi.org/10.1007/s00010-014-0267-5
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00010-014-0267-5