We study the existence and uniqueness theorem for solving the generalized operator equation of the form $F(x)+G(x)+T(x)\ni 0$, where F is a Fr\'echet differentiable operator, $G$ is a maximal monotone operator and $T$ is a Lipschitzian operator defined on an open convex subset of a Hilbert space. Our results are improvements upon corresponding results of Uko [Generalized equations and the generalized Newton method, Math. Programming 73 (1996) 251-268].