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

Subject Areas : Difference and functional equations

P. Kaskasem ¹ , C. Klin-eam ²

1 - Department of Mathematics, Faculty of Science Naresuan University, Phitsanulok, 65000, Thailand
2 - Research center for Academic Excellence in Mathematics, Naresuan University, Phitsanulok, Thailand

Received: 2019-05-22 Accepted : 2019-10-29 Published : 2020-03-01

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

Abstract :

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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