Jordan derivations on $C^*$-ternary algebras for a Cauchy-Jensen functional equation

TL;DR

This paper establishes the stability of homomorphisms and derivations in $C^*$-ternary algebras related to a specific Cauchy-Jensen functional equation, and explores their isomorphisms.

Contribution

It proves the generalized Hyers-Ulam stability for homomorphisms and derivations in $C^*$-ternary algebras for the Cauchy-Jensen equation, and investigates algebra isomorphisms.

Findings

Proved stability of homomorphisms in $C^*$-ternary algebras.

Established stability of derivations in $C^*$-ternary algebras.

Applied results to characterize isomorphisms between $C^*$-ternary algebras.

Abstract

In this paper, we proved the generalized Hyers-Ulam stability of homomorphisms in $C^*$- ternary algebras and of derivations on $C^*$-ternary algebras for the following Cauchy- Jensen functional equation $$3f\bigg(\frac{x+y+z}{3}\bigg)=2f\bigg(\frac{x+y}{2}\bigg)+f(z).$$ These were applied to investigate isomorphisms between $C^*$-ternary algebras.