Generalized quadratic mappings in several variables Original Research Article

Let X,Y be vector spaces. It is shown that if an even mapping View the MathML source satisfies f(0)=0, and equation(0.1) View the MathML source for all x1,…,xd∈X, then the even mapping View the MathML source is quadratic. Furthermore, we prove the Cauchy–Rassias stability of the functional equation (0.1) in Banach spaces.