Stability of generalized Newton difference equations

In the paper we discuss a stability in the sense of the generalized Hyers-Ulam-Rassias for functional equations Δⁿ_{(p, c)}φ(x) = h(x), which is called generalized Newton difference equations, and give a sufficient condition of the generalized Hyers-Ulam-Rassias stability. As corollaries, we obtain the generalized Hyers-Ulam-Rassias stability for generalized forms of square root spirals functional equations and general Newton functional equations for logarithmic spirals.