On the Drygas functional equation in restricted domains

Let ({{mathbb{R}}}) and Y be the set of real numbers and a Banach space respectively, and ({f, g :{mathbb{R}} to Y}). We prove the Ulam-Hyers stability theorems for the Pexider-quadratic functional equation ({f(x + y) + f(x - y) = 2f(x) + 2g(y)}) and the Drygas functional equation ({f(x + y) + f(x - y) = 2f(x) + f(y) + f(-y)}) in the restricted domains of form ({Gamma_d := Gamma cap {(x, y) in {mathbb{R}}^2 : |x| + |y| ge d}}), where ({Gamma}) is a rotation of ({B times B subset {mathbb{R}}^2}) and ({B^c}) is of the first category. As a consequence we obtain asymptotic behaviors of the equations in a set ({Gamma_d subset {mathbb{R}}^2}) of Lebesgue measure zero.