Nearly Jordan -Homomorphisms between Unital -Algebras

Let , be two unital ∗-algebras. We prove that every almost unital almost linear mapping ℎ : → which satisfies ℎ(3+3)=ℎ(3)ℎ()+ℎ()ℎ(3) for all ∈(), all ∈, and all =0,1,2,…, is a Jordan homomorphism. Also, for a unital ∗-algebra of real rank zero, every almost unital almost linear continuous mapping ℎ∶→ is a Jordan homomorphism when ℎ(3+3)=ℎ(3)ℎ()+ℎ()ℎ(3) holds for all ∈1 (sa), all ∈, and all =0,1,2,…. Furthermore, we investigate the Hyers- Ulam-Aoki-Rassias stability of Jordan ∗-homomorphisms between unital ∗-algebras by using the fixed points methods

On the stability of J∗−^*-derivations

In this paper, we establish the stability and superstability of $J^*-$derivations in $J^*-$algebras for the generalized Jensen--type functional equation $$rf(\frac{x+y}{r})+rf(\frac{x-y}{r})= 2f(x).$$ Finally, we investigate the stability of $J^*-$derivations by using the fixed point alternative

Approximately <inline-formula> <graphic file="1029-242X-2009-870843-i1.gif"/></inline-formula>-Jordan Homomorphisms on Banach Algebras

Let , and let be two rings. An additive map is called -Jordan homomorphism if for all . In this paper, we establish the Hyers-Ulam-Rassias stability of -Jordan homomorphisms on Banach algebras. Also we show that (a) to each approximate 3-Jordan homomorphism from a Banach algebra into a semisimple commutative Banach algebra there corresponds a unique 3-ring homomorphism near to , (b) to each approximate -Jordan homomorphism between two commutative Banach algebras there corresponds a unique -ring homomorphism near to for all .</p

Solution and stability of a mixed type additive, quadratic, and cubic functional equation

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)

Solution and Stability of a Mixed Type Additive, Quadratic, and Cubic Functional Equation

<p/> <p>We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the mixed type additive, quadratic, and cubic functional equation <inline-formula><graphic file="1687-1847-2009-826130-i1.gif"/></inline-formula>.</p

Stability of an Additive-Cubic-Quartic Functional Equation

In this paper, we consider the additive-cubic-quartic functional equation 11[f(x+2y)+f(x&#x2212;2y)]=44[f(x+y)+f(x&#x2212;y)]+12f(3y)&#x2212;48f(2y)+60f(y)&#x2212;66f(x) and prove the generalized Hyers-Ulam stability of the additive-cubic-quartic functional equation in Banach spaces