Document Type : Research Paper

Author

• Ismail Nikoufar

Department of Mathematics, Payame Noor University, Tehran, Iran

Abstract

In the Hyers-Ulam-Rassias stability depending on the type of the function whose stability we want to verify a suitable functional equation is used. The authors in [6] want to investigate the Hyers-Ulam-Rassias stability of $n$-Jordan $C^*$-homomorphisms on $C^*$-algebras, but they used a quadratic functional equation while we know that the homomorphisms are linear on $C^*$-algebras. In this paper, we correct the main results of  [6]  by removing the quadratic functional equation and replacing the linear one and removing some extra conditions. We also show that by using some other multi-variable linear functional equations, the estimation becomes better and more accurate.

Keywords

• Hyers-Ulam-Rassias stability
• $n$-jordan $C^*$-homomorphism
• $n$-jordan homomorphism
• $C^*$-algebra