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

In 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.  2004 Elsevier Inc. All rights reserved