On Stability of the Cauchy Equation on Solvable Groups

• Date: 2015
• Main Authors: Faiziev, V. A., Sahoo, P. K., Файзієв, В. А., Сахо, П. К.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2015
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2039
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...