## Bulletin of the Belgian Mathematical Society - Simon Stevin

### On the Stability of Cauchy Additive Mappings

#### Abstract

It is well-known that the concept of Hyers-Ulam-Rassias stability originated by Th. M. Rassias (Proc. Amer. Math. Soc. 72(1978), 297-300) and the concept of Ulam-Gavruta-Rassias stability by J. M. Rassias (J. Funct. Anal. U.S.A. 46(1982), 126-130; Bull. Sc. Math. 108 (1984), 445-446; J. Approx. Th. 57 (1989), 268-273) and P. Gavruta (An answer to a question of John M. Rassias concerning the stability of Cauchy equation", in: Advances in Equations and Inequalities, in: Hadronic Math. Ser. (1999), 67-71). In this paper we give results concerning these two stabilities.

#### Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 15, Number 3 (2008), 391-402.

Dates
First available in Project Euclid: 30 September 2008

https://projecteuclid.org/euclid.bbms/1222783087

Digital Object Identifier
doi:10.36045/bbms/1222783087

Mathematical Reviews number (MathSciNet)
MR2457956

Zentralblatt MATH identifier
1156.39018

#### Citation

Jun, Kil-Woung; Roh, Jaiok. On the Stability of Cauchy Additive Mappings. Bull. Belg. Math. Soc. Simon Stevin 15 (2008), no. 3, 391--402. doi:10.36045/bbms/1222783087. https://projecteuclid.org/euclid.bbms/1222783087