Fixed points and fuzzy stability of an additive-quadratic functional equation
The fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated by Moslehian et al. Using fixed point method, we prove the Hyers-Ulam stability of the functional equation
APPROXIMATION OF GENERALIZED HOMOMORPHISMS IN QUASI–BANACH ALGEBRAS
Let A be a quasi–Banach algebra with quasi-norm k .k A and B be a p-Banach algebra with p-norm k .k B. A linear mapping f : A → B is called a generalized homomorphism if there exists a homomorphism h ′ : A → B such that f(ab) = f(a)h ′ (b) for all a, b ∈ A. In this paper, we investigate generalized homomorphisms on quasi– Banach algebras, associated with the following functional equation rf( a + b r ) = f(a) + f(b). Moreover, we prove the generalized Hyers–Ulam–Rassias stability and superstability of generalized homomorphisms in quasi–Banach algebras.
On approximate ring homomorphisms
We prove the stability of a generalization of the Bourgin's result on approximate ring homomorphisms.