A generalization of the Hyers–Ulam–Rassias stability of the Pexiderized quadratic equations

AbstractIn this paper we prove the Hyers–Ulam–Rassias stability by considering the cases that the approximate remainder ϕ is defined by f(x∗y)+f(x∗y−1)−2g(x)−2g(y)=ϕ(x,y), f(x∗y)+g(x∗y−1)−2h(x)−2k(y)=ϕ(x,y), where (G,∗) is a group, X is a real or complex Hausdorff topological vector space and f,g,h,k are functions from G into X