Approximation of the generalized Cauchy–Jensen functional equation in C∗ $C^{*}$-algebras

Journal of Inequalities and Applications

Prondanai Kaskasem¹  Chakkrid Klin-eam¹ 

[1] Department of Mathematics, Faculty of Science, Naresuan University;

关键词: Cauchy–Jensen functional equations;    Hyers–Ulam–Rassias stability;    C ∗ $C^{*}$ -algebras;    Fixed point theorem;   

DOI  :  10.1186/s13660-018-1824-6

来源: DOAJ

【 摘 要 】

Abstract In this paper, we prove Hyers–Ulam–Rassias stability of C∗ $C^{*}$-algebra homomorphisms for the following generalized Cauchy–Jensen equation: αμf(x+yα+z)=f(μx)+f(μy)+αf(μz), $$ \alpha\mu f \biggl(\frac{x+y}{\alpha}+z \biggr) = f(\mu x) + f(\mu y) +\alpha f( \mu z), $$ for all μ∈S:={λ∈C∣|λ|=1} $\mu\in\mathbb{S}:= \{ \lambda\in\mathbb{C} \mid|\lambda| =1\}$ and for any fixed positive integer α≥2 $\alpha\geq2$, which was introduced by Gao et al. [J. Math. Inequal. 3:63–77, 2009], on C∗ $C^{*}$-algebras by using fixed poind alternative theorem. Moreover, we introduce and investigate Hyers–Ulam–Rassias stability of generalized θ-derivation for such functional equations on C∗ $C^{*}$-algebras by the same method.

【 授权许可】

Unknown