Approximate solutions of homomorphisms and derivations of the generalized Cauchy-Jensen functional equation in $C^*$-ternary algebras

محورهای موضوعی : Difference and functional equations

P. Kaskasem ¹ (Department of Mathematics, Faculty of Science Naresuan University, Phitsanulok, 65000, Thailand)
C. Klin-eam ² (Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, Thailand)

تاریخ دریافت : 1398/03/01 تاریخ پذیرش : 1398/08/07 تاریخ انتشار : 1398/12/11

کلید واژه: Hyers-Ulam-Rassias stability, Cauchy-Jensen functional equations, C*-ternary algebras, alternative fixed point theorem,

چکیده مقاله :

In this paper, we prove Hyers-Ulam-Rassias stability of $C^*$-ternary algebra homomorphism for the following generalized Cauchy-Jensen equation $$\eta \mu f\left(\frac{x+y}{\eta}+z\right) = f(\mu x) + f(\mu y) +\eta f(\mu z)$$ for all $\mu \in \mathbb{S}:= \{ \lambda \in \mathbb{C} : |\lambda | =1\}$ and for any fixed positive integer $\eta \geq 2$ on $C^*$-ternary algebras by using fixed poind alternative theorem. Moreover, we investigate Hyers-Ulam-Rassias stability of generalized $C^*$-ternary derivation for such function on $C^*$-algebras by the same method.

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