New w-Convergence Conditions for the Newton-Kantorovich Method

Authors

  • Ioannis K. Argyros Department of Mathematicsal Sciences, Cameron University, Lawton, OK 73505, USA.
  • Hongmin Ren College of Information and Engineering, Hangzhou Polytechnic, Hangzhou 311402, Zhejiang, PR China.

Keywords:

Newton-Kantorovich method, Banach space, majorizing series, telescopic series

Abstract

We present new sufficient semilocal convergence conditions for the Newton-Kantorovich method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. Examples are given to show that our results apply but earlier ones do not apply to solve nonlinear equations.

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Published

2014-06-30

Issue

Vol. 46 No. 1 (2014)

Section

Articles

License

Copyright (c) 2014 Ioannis K. Argyros, Hongmin Ren

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

How to Cite

New w-Convergence Conditions for the Newton-Kantorovich Method. (2014). Punjab University Journal of Mathematics, 46(1), 74-83. https://pujm.pu.edu.pk/index.php/pujm/article/view/26