Abstract
In this paper, we study the existence and uniqueness theorem for solving the generalized operator equation of the form F(x) + G(x) + T(x) ? 0, where F is a Fr?chet 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].
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