Stability of an incomplete gamma-type functional equation

We investigate the Hyers-Ulam-Rassias stability of an incomplete gamma-type functional equation f(phi(1)(x(1)),center dot center dot center dot, phi n(x(n)), psi(1)(y(1)),center dot center dot center dot, psi(m)(y(m))) = 0(x(1),center dot center dot center dot, x(n), y(1),center dot center dot center dot, y(m))f(x(1),center dot center dot center dot, x(n), y(1),center dot center dot center dot, y(m)) + lambda(x(1),center dot center dot center dot, x(n), y(1),center dot center dot center dot y(m)) with a restricted domain. By this result we obtain the stability of the incomplete gamma functional equation f(x + 1, y) = xf(x, y) + e(-y)(y)(x) with a restricted domain.