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Let A be an algebra and X be an A-module. A quadratic mapping D : A → X is called a quadratic derivation if D(ab) = D(a)b² + a²D(b) for all a1, a2 ∈ A. We investigate the Hyers-Ulam stability of quadratic derivations from a non-Archimedean Banach algebra A into a non-Archimedean Banach A-module. [ABSTRACT FROM AUTHOR]

Let A be a ternary Banach algebra with norm ||-||A and B be a ternary Banach algebra with norm ||-||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⊃] + [x⊃2, D(y), z⊃2] + [x⊃2, y⊃2, D(z)] for all x, y, z ∈ 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) + 2f(y). Moreover, we prove the generalized Hyers-Ulam-Rassias stability of ternary quadratic derivations on ternary Banach algebras. [ABSTRACT FROM AUTHOR]

Let A, B be two ternary algebras. A mapping H : A → B is called a ternary cubic homomorphism if H is a cubic function, which satisfies: H([x, y, z]) = [H(x), H(y), H(z)] for all x, y, z ∈ A. In this paper, we investigate ternary cubic homomorphisms on ternary Fréchet algebras. [ABSTRACT FROM AUTHOR]

Using fixed point methods, we investigate the stability of n-Jordan homomorphisms (n-Jordan "-homomorphisms) on Banach algebras (C"-algebras). [ABSTRACT FROM AUTHOR]