Stability of homomorphisms and derivations in \(C^*\)-ternary rings
The stability problem dealing with ternary structures was investigated by \textit{M. S. Moslehian} [Bull. Belg. Math. Soc. - Simon Stevin 14, No.~1, 135--142 (2007; Zbl 1132.39026) and Bull. Braz. Math. Soc. (N.S.) 38, No.~4, 611--622 (2007; Zbl 1141.39029)]. In this paper the authors study the Hyers-Ulam-Rassias stability of homomorphisms in \(C^*\)-ternary rings and of derivations on \(C^*\)-ternary rings for the below functional equation of generalized Cauchy-Jensen additive type \[ 2f \left(\frac{\sum_{j=1}^p x_j+\sum_{j=1}^q y_j}{2}+\sum_{j=1}^d z_j \right)= \sum_{j=1}^pf(x_j)+\sum_{j=1}^q f(y_j)+2\sum_{j=1}^d f(z_j), \] where \(p, q, d\) are nonnegative integers with \(p+q+d\geq 3\).
generalized Cauchy-Jensen functional equation
scientific article; zbMATH DE number 5734712