摘要：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) + 16g(y) + 16g(z) = 8[g(x + y) + g(x − y) + g(x + z) + g(x − z)] + 2[g(y + z) + g(y − z)] + 32g(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)] + 32f(x) (2) for all x,y,z ∈ X with x ⊥ y,y ⊥ z and z ⊥ x is discussed in orthogonality space in the sense of Rätz.
