Approximation of derivations and the superstability in random Banach -algebras

Abstract

We prove that approximations of derivations on random Banach *-algebras are exactly derivations by using a fixed point method. Furthermore, we show that approximations of quadratic *-derivations on random Banach *-algebras are exactly quadratic *-derivations. We, moreover, prove that approximations of derivations on random C *-ternary algebras are exactly derivations by using a fixed point method.