Abstract
Beginning around the year 1980, the topic of approximate homomorphisms and derivations and their stability theory in the field of functional equations and inequalities was taken up by several mathematicians (see Hyers and Rassias, Aequat Math 44:125–153, 1992; Rassias, Acta Appl Math 62:23–130, 2000 and the references therein).
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Ara, P., Mathieu, M.: Local Multipliers of C ∗-Algebras. Springer, London (2003)
Baak, C.: Cauchy-Rassias stability of Cauchy-Jensen additive mappings in Banach spaces. Acta Math. Sin. 22, 1789–1796 (2006)
Eskandani, G.Z.: On the Hyers-Ulam-Rassias stability of an additive functional equation in quasi-Banach spaces. J. Math. Anal. Appl. 345, 405–409 (2008)
Hyers, D.H., Rassias, Th.M.: Approximate homomorphisms. Aequ. Math. 44, 125–153 (1992)
Jun, K.W., Kim, H.M., Rassias, J.M.: Extended Hyers-Ulam stability for Cauchy-Jensen mappings. J. Differ. Equ. Appl. 13, 1139–1153 (2007)
Lee, S.H., Park, C.: Hyers-Ulam-Rassias stability of isometric homomorphisms in quasi-Banach algebras. J. Comput. Anal. Appl. 10, 39–51 (2008)
Park, C.: Hyers-Ulam-Rassias stability of a generalized Euler-Lagrange type additive mapping and isomorphisms between C ∗-algebras. Bull. Belg. Math. Soc.–Simon Stevin 13, 619–631 (2006)
Park, C.: Fixed points and Hyers-Ulam-Rassias stability of Cauchy-Jensen functional equations in Banach algebras. Fixed Point Theory Appl. 2007, Article ID 50175 (2007)
Park, C.: Hyers-Ulam-Rassias stability of homomorphisms in quasi-Banach algebras. Bull. Sci. Math. 132, 87–96 (2008)
Park, C., An, J.S.: Isomorphisms in quasi-Banach algebras. Bull. Korean Math. Soc. 45, 111–118 (2008)
Rassias, Th.M.: On the stability of the linear mapping in Banach spaces. Proc. Am. Math. Soc. 72, 297–300 (1978)
Rassias, Th.M.: On the stability of functional equations and a problem of Ulam. Acta Appl. Math. 62, 23–130 (2000)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Cho, Y.J., Park, C., Rassias, T.M., Saadati, R. (2015). Stability of Functional Equations in Banach Algebras. In: Stability of Functional Equations in Banach Algebras. Springer, Cham. https://doi.org/10.1007/978-3-319-18708-2_2
Download citation
DOI: https://doi.org/10.1007/978-3-319-18708-2_2
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-18707-5
Online ISBN: 978-3-319-18708-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)