APPROXIMATE QUADRATIC FORMS ON RESTRICTED DOMAINS

摘要

Let r, s be nonzero real numbers with r + s = 1. In [9], Najati and Jung investigated a quadratic functional equation g(rx + sy) + rs g(x - y) = r g(x) + sg(y). We introduce a functional equation f (rx + sy, rz + sw) + rs f (x - y, z - w) = r f (x, z) + s f (y, w) and investigate the relation between the above two functional equations. And we find out the general solution and the Hyers-Ulam stability of the latter on restricted domains.