Zeitschrift für Analysis und ihre Anwendungen Vol. 18, No. 3, pp. 785792 (1999) 

Concerning the Convergence of a Modified NewtonLike MethodIoannis K. ArgyrosI. K. Argyros: Cameron Univ., Dept. Math., Lawton, OK 73505, U.S.A.Abstract: We provide sufficient convergence conditions for a certain Newtonlike method to a locally unique solution of a nonlinear equation in a Banach space. We assume that the Fréchetderivative of the operator involved satisfies in some sense uniformly continuous conditions, which are weaker than earlier ones. We show that our results apply where earlier ones fail. Finally, we solve a nonlinear integral equation of Urysontype that cannot be solved using Proposition 2 in [10]. Keywords: modified Newtonlike method, Banach spaces, Uryson integral equations, uniformly continuity Classification (MSC2000): 65J15, 65B05, 47H17, 49D15 Full text of the article:
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