Stability of a Quartic and Orthogonally Quartic Functional Equation
نویسنده
چکیده
In this paper, the authors investigate the generalized Hyers-UlamAoki-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.
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تاریخ انتشار 2011