STABILITY OF TERNARY QUADRATIC DERIVATION ON TERNARY BANACH ALGEBRAS
Let A be a ternary Banach algebra with norm parallel to.parallel to(A) and B be a ternary Banach algebra with norm parallel to.parallel to(B). A mapping D : A -> B is called a ternary quadratic derivation if D be a quadratic function, D[x, y, z] = [D(x), y(2), z(2)] + [x(2), D(y), z(2)] + [x(2), y(2), D(z)] for all x, y, z is an element of A. In this paper, we investigate ternary quadratic derivation on ternary Banach algebras, associated with the following functional equation f (x + y) + f (x - y) = 2f(x) + 2 f (y). Moreover, we prove the generalized Hyers-Ulam-Rassias stability of ternary quadratic derivations on ternary Banach algebras.
ternary quadratic derivation ternary banach algebra generalized hyers-ulam-rassias stability quadratic functional equation