Concerning the Convergence of a Modified Newton-Like Method | Zendy

Ioannis K. Argyros | Zendy

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Concerning the Convergence of a Modified Newton-Like Method

Author(s) -

Ioannis K. Argyros

Publication year - 1999

Publication title -

zeitschrift für analysis und ihre anwendungen

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.567

H-Index - 35

eISSN - 1661-4534

pISSN - 0232-2064

DOI - 10.4171/zaa/913

Subject(s) - convergence (economics) , mathematics , newton's method , calculus (dental) , physics , economics , medicine , nonlinear system , orthodontics , quantum mechanics , economic growth

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].

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