A simplified proof of the Kantorovich theorem for solving equations using telescopic series

Authors

  • Ioannis K. Argyros Cameron University, USA
  • Hongmin Ren Hangzhou Polytechnic, China

DOI:

https://doi.org/10.33993/jnaat442-1084

Keywords:

Newton-Kantorovich method, Banach space, majorizing series, telescopic series, Kantorovich theorem
Abstract views: 275

Abstract

We extend the applicability of the Kantorovich theorem (KT) for solving nonlinear equations using Newton-Kantorovich method in a Banach space setting. Under the same information but using elementary scalar telescopic majorizing series, we provide a simpler proof for the (KT) [2], [7]. Our results provide at least as precise information on the location of the solution. Numerical examples are also provided in this study.

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Author Biography

Ioannis K. Argyros, Cameron University, USA

Full tenured Professor of Mathematics.

References

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Published

2015-12-31

How to Cite

Argyros, I. K., & Ren, H. (2015). A simplified proof of the Kantorovich theorem for solving equations using telescopic series. J. Numer. Anal. Approx. Theory, 44(2), 146–153. https://doi.org/10.33993/jnaat442-1084

Issue

Vol. 44 No. 2 (2015)

Section

Articles

License

Copyright (c) 2016 Journal of Numerical Analysis and Approximation Theory

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