STABILITY OF A QUARTIC AND ORTHOGONALLY QUARTIC FUNCTIONAL EQUATION

In this paper, the authors investigate the generalized Hyers-Ulam-Aoki-Rassias stability of a quartic functional equation g(2x + y + z) + g(2x + y - z) + g(2x - y + z) + g(-2x + y + z) + 16 g(y) + 16 g(z) = 8[g(x + y) + g(x -y) + g(x + z) + g(x - z)] + 2[g(y + z) + g(y - z)] + 32 g(x). (1) The above equation(1) is modified and its Hyers-Ulam-Aoki-Rassias stability for the following quartic functional equation f(2x + y + z) + f(2x + y - z) + f(2x - y + z) + f(-2x + y + z) + f(2y) + f(2z) = 8[f(x + y) + f(x - y) + f(x + z) + f(x - z)] + 2[f(y + z) + f(y - z)] + 32 f(x) (2) for all x, y, z. X with x perpendicular to y, y perpendicular to z and z perpendicular to x is discussed in orthogonality space in the sense of Ratz.