Communications of the
Korean Mathematical Society CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024
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Commun. Korean Math. Soc. 2011; 26(4): 575-584

Printed December 1, 2011

https://doi.org/10.4134/CKMS.2011.26.4.575

Copyright © The Korean Mathematical Society.

On the convergence of a Newton-like method under weak conditions

Ioannis K. Argyros and Hongmin Ren

Cameron University, Hangzhou Radio and TV University

Abstract

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We provide a semilocal convergence analysis for a Newton-like method under weak conditions in a Banach space setting. In particular, we only assume that the Gateaux derivative of the operator involved is hemicontinuous. An application is also provided.

Keywords: Newton-like method, Banach space setting, semilocal convergence, Gateaux-derivative, hemicontinuity

MSC numbers: 65G99, 65J15, 47H17, 49M15

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