APPROXIMATELY n-MULTIPLICATIVE AND APPROXIMATELY ADDITIVE FUNCTIONS IN NORMED ALGEBRAS

We derive some properties of (epsilon, delta, n)-multiplicative maps between normed algebras and establish the superstability of (delta, n)-multiplicative functionals on normed algebras. We also prove that if phi is an (epsilon, delta, n)-multiplicative such that in the case where n is odd, 1 is an element of phi(A), then vertical bar vertical bar vertical bar phi vertical bar vertical bar vertical bar <= (1+delta)(1/(n-1)). Moreover, under certain conditions, we prove that if phi : A -> C-0(X) is an (epsilon, delta, n)-multiplicative, then vertical bar vertical bar vertical bar phi vertical bar vertical bar vertical bar <= (1+delta)(1/(n-1)), where C-0(X) is the algebra of all real valued continuous functions which vanish at infinity defined on a locally compact Hausdorff space X.