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Let A be a unital C*-algebras, B be a Banach algebra and let X be a Banach A-module. By using fixed point methods, we prove that: i) Every almost linear mapping h : A → B which satisfies h(2nuy) = h(2nu)h(y) for all u ∈ A+, all y ∈ A, and all n = 0, 1,2,…, is a homomorphism. ii) Every almost linear continuous mapping d : A → X is a derivation when d(2nuy) = d(2nu)y + 2nud(y) holds for all u ∈ A+, all u ∈ A, and all n = 0, 1, 2,…. [ABSTRACT FROM AUTHOR]

Let A, B be two unital C*-algebras. We prove that every almost unital almost linear mapping h : A → B which satisfies h(3nuy+3nyu) = h(3nu)h(y)+h(y)h(3nu) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2,…, is a Jordan homomorphism. Also, for a unital C*-algebra A of real rank zero, every almost unital almost linear continuous mapping h : A → B is a Jordan homomorphism when h(3nuy+3nyu) = h(3nu)h(y)+h(y)h(3nu) holds for all u ∈ I1 (Asa), all y ∈ A, and all n = 0, 1, 2,…. Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan *-homomorphisms between unital C*-algebras by using the fixed points methods. [ABSTRACT FROM AUTHOR]

We say a functional equation (ξ) is stable if any function g satisfying the equation (ξ) approximately is near to true-solution of (ξ). In this paper, we prove the Generalized Hyers-Ulam stability of ternary Jordan *-derivations in C* -ternary algebras for the following generalized Cauchy-Jensen additive mapping: rƒ(sΣj=1p xj + t Σj=1d xj/r = s Σj=1p ƒ(xj) + t Σj=1d ƒ(xj). [ABSTRACT FROM AUTHOR]

We say a functional equation (ξ) is stable if any function g satisfying the equation (ξ) approximately is near to true solution of (ξ). In this paper, we prove the Generalized Hyers-Ulam stability of ternary Jordan *-derivations in C*-ternary algebras for the following generalized Cauchy-Jensen additive mapping: (These equations cannot be represented into ASCII text). [ABSTRACT FROM AUTHOR]

We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the mixed type additive, quadratic, and cubic functional equation f (x + 2y) - f (x - 2y) = 2 (f (x + y) - f (x - y)) + 2f (3y) - 6f (2y) + 6f (y). [ABSTRACT FROM AUTHOR]

Let n ϵ N, and let A, B be two rings. An additive map h : A → B is called n-Jordan homomorphism if h(an) = (h(a))n for all a ϵ A. In this paper, we establish the Hyers-Ulam-Rassias stability of n-Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism h from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to f, (b) to each approximate n-Jordan homomorphism h between two commutative Banach algebras there corresponds a unique n-ring homomorphism near to f for all n ϵ (3, 4, 5). [ABSTRACT FROM AUTHOR]