the aim of this paper is to show that under some mild conditions a functional equation of multiplicative (; )-derivation is superstable on standard operator algebras. furthermore, we prove that this generalized derivation can be a continuous and an inner (; )- derivation.

In this work, by using some orthogonally fixed point theorem, we prove the stability and hyperstability of C ∗ -ternary Jordan homomorphisms between id="M3"> Banach algebras id="M4"> derivations functional equation on id="M5"> algebras.