Homomorphisms and Derivations in C∗-Ternary Algebras

Abstract

In 2006, C. Park proved the stability of homomorphisms in $C^{\ast }$-ternary algebras and of derivations on $C^{\ast }$-ternary algebras for the following generalized Cauchy-Jensen additive mapping: $2f\left(\left({\sum }_{j=1}^p{x}_j/2\right)+{\sum }_{j=1}^d{y}_j\right)={\sum }_{j=1}^{p}f\left(x_j\right)+2{\sum }_{j=1}^{d}f\left(y_j\right)$. In this note, we improve and generalize some results concerning this functional equation.