Approximately Ternary Homomorphisms and Derivations on C

We investigate the stability and superstability of ternary homomorphisms between C*-ternary algebras and derivations on C*-ternary algebras, associated with the following functional equation f((x2-x1)/3)+f((x1-3x3)/3)+f((3x1+3x3-x2)/3)=f(x1)

Generalized Hyers-Ulam Stability of Generalized (,)-Derivations

Let 3≤, and 3≤≤ be positive integers. Let be an algebra and let be an -bimodule. A ℂ-linear mapping ∶→ is called a generalized (,)-derivation if there exists a (−1)-derivation ∶→ such that (12⋯)=(1)2⋯+1(2)3⋯+⋯+12⋯−2(−1)⋯+12⋯−1()+1⋯+12⋯(+1)+2⋯+12⋯+1(+2)+3⋯+⋯+1⋯−1() for all 1,2,…,∈. The main purpose of this paper is to prove the generalized Hyers-Ulam stability of the generalized (,)-derivations