Generalized Newton Iterative Methods for Nonlinear Operator Equations

  • Livinus U. Uko
  • J.O. Adeyeye


The generalized Newton schemes are extensions of the classical Newton's method based on partial linearization. Introduced by Josephy in the seventies, such methods have been generalized in recent years by several authors and applied to different classes of problems. In the present paper we study some generalized Newton methods for the iterative solution of smooth operator equations in Banach spaces. We use the method of nondiscrete induction to give a Kantorovich-type convergence result for a general iterative scheme which contains as special cases several generalized Newton schemes that have appeared in the literature. We also discuss some possible applications of these methods.