# On Stability of the Cauchy Equation on Solvable Groups

### Abstract

The notion of $(ψ, γ)$-stability was introduced in [V. A. Faiziev, Th. M. Rassias, and P. K. Sahoo,*Trans. Amer. Math. Soc.*, 354, 4455 (2002)]. It was shown that the Cauchy equation $f (xy) = f (x) + f (y)$ is $(ψ, γ)$-stable both on any Abelian group and on any meta-Abelian group. In [V. A. Faiziev and P. K. Sahoo,

*Publ. Math. Debrecen*, 75, 6 (2009)], it was proved that the Cauchy equation is $(ψ, γ)$-stable on step-two solvable groups and step-three nilpotent groups. In the present paper, we prove a more general result and show that the Cauchy equation is $(ψ, γ)$-stable on solvable groups.

Published

25.07.2015

How to Cite

*Ukrains’kyi Matematychnyi Zhurnal*, Vol. 67, no. 7, July 2015, pp. 1000-5, http://umj.imath.kiev.ua/index.php/umj/article/view/2039.

Issue

Section

Short communications