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Let A,B be two unital C*-algebras. By using fixed pint methods, we prove that every almost unital almost linear mapping h: A → B which satisfies h(2nuy)= h(2nu)h(y) for all u ∈ U(A), all y ∈ A, and all n=0,1,2, …, is a homomorphism. Also, we establish the generalized Hyers-Ulam-Rassias stability of *-homomorphisms on unital C*-algebras.

In this paper, we achieve the general solution and the generalized Hyres–Ulam–Rassias stability of the following additive–quadratic functional equation $$f (x + ky) + f (x - ky) = f (x + y) + f (x - y) + \frac{2(k + 1)}{k} f (ky) - 2(k + 1)f (y)$$ for fixed integers k with k ≠ 0, ±1 in non-Archimedean spaces.

In this note, we prove the Hyers-Ulam-Rassias stability of Jordan homomorphisms in C ⁄ iternary algebras for the following generalized Cauchy

Dedicated to Themistocles M. Rassias on the occasion of his sixtieth birthday Abstract. In this paper, we investigate Jordan homomorphisms in proper JCQ ⁄ -triples associated with the generalized 3-variable Jesnsen functional equation rf( x + y + z r ) = f(x) + f(y) + f(z); with r 2 (0;3) n f1g. We moreover prove the Hyers-Ulam-Rassias stability of Jordan homomorphisms in proper JCQ ⁄ -triples.

We find the general solution of the functional equation $$\begin{array}{l} D_f {\rm{(}}x,y{\rm{)}}\,\,{\rm{: = }}f{\rm{(}}x + {\rm{2}}y{\rm{)}} + f{\rm{(}}x - {\rm{2}}y{\rm{)}} - {\rm{4[}}f{\rm{(}}x + y{\rm{)}} - f{\rm{(}}x - y{\rm{)]}} - f{\rm{(4}}y{\rm{)}} + {\rm{4}}f{\rm{(3}}y{\rm{)}} \\ - {\rm{6}}f{\rm{(2}}y{\rm{)}} + {\rm{4}}f{\rm{(}}y{\rm{)}} + {\rm{6}}f{\rm{(}}x{\rm{) }} = {\rm{ 0}}{\rm{.}} \\ \end{array}$$ in the context of linear spaces. We prove that if a mapping f from a linear space X into a Banach space Y satisfies f(0)=0 and $$\|D_f(x,y)\|\leq\epsilon \quad (x,y\in X),$$ where e > 0, then there exist a unique additive mapping \(A:X\to Y,\) a unique quadratic mapping \(Q_1:X\to Y,\) a unique cubic mapping \(C:X\to Y\) and a unique quartic mapping \(Q_2:X\to Y\) such that $$\|f(x)-A(x)-Q_1(x)-C(x)-Q_2(x)\|\leq\frac{1087 \epsilon}{140}\quad \forall x\in X.$$

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.

We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the mixed type additive, quadratic, and cubic functional equation .