Approximation of derivations and the superstability in random Banach a??-algebras

摘要

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