Poisson C*-algebra derivations in Poisson C*-algebras

Abstract

In this study, we introduce the following additive functional equation:g(λu+v+2y)=λg(u)+g(v)+2g(y)g\left(\lambda u+v+2y)=\lambda g\left(u)+g\left(v)+2g(y) for all λ∈C\lambda \in {\mathbb{C}}, all unitary elements u,vu,v in a unital Poisson C*{C}^{* }-algebra PP, and all y∈Py\in P. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the aforementioned additive functional equation in unital Poisson C*{C}^{* }-algebras. Furthermore, we apply to study Poisson C*{C}^{* }-algebra homomorphisms and Poisson C*{C}^{* }-algebra derivations in unital Poisson C*{C}^{* }-algebras.

Keywords

• hyers-ulam stability
• fixed point method
• additive functional equation
• poisson c *-algebra derivation in poisson c *-algebra
• poisson c *-algebra homomorphism in poisson c *-algebra
• 47b47
• 17b63
• 17b40
• 39b72
• 46l05
• 47h10
• 39b52