On Stability of the Cauchy Equation on Solvable Groups

  • V. A. Faiziev
  • P. K. Sahoo

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
FaizievV. A., and SahooP. K. “On Stability of the Cauchy Equation on Solvable Groups”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 67, no. 7, July 2015, pp. 1000-5, http://umj.imath.kiev.ua/index.php/umj/article/view/2039.
Section
Short communications