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Zeitschrift für Analysis und ihre Anwendungen

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Volume 18, Issue 3, 1999, pp. 785–792
DOI: 10.4171/ZAA/913

Published online: 1999-09-30

Concerning the Convergence of a Modified Newton-Like Method

Ioannis K. Argyros[1]

(1) Cameron University, Lawton, USA

We provide sufficient convergence conditions for a certain Newton-like method to a locally unique solution of a nonlinear equation in a Banach space. We assume that the Fréchet-derivative 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 Uryson-type that cannot be solved using Proposition 2 in [10].

Keywords: Modified Newton-like method, Banach spaces, Uryson integral equations, uniformly continuity

Argyros Ioannis: Concerning the Convergence of a Modified Newton-Like Method. Z. Anal. Anwend. 18 (1999), 785-792. doi: 10.4171/ZAA/913