On the convergence of a Newton-like method under weak conditions
Commun. Korean Math. Soc. 2011 Vol. 26, No. 4, 575-584
https://doi.org/10.4134/CKMS.2011.26.4.575
Published online December 1, 2011
Ioannis K. Argyros and Hongmin Ren
Cameron University, Hangzhou Radio and TV University
Abstract : 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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