Strong convergence theorem of a new iterative method for weak contractions and comparison of the rate of convergence in Banach space
Abstract
In this paper, we first construct a new iteration method for approximating fixed points of a class of weak contractions in a Banach space and then prove strong convergence theorem of the proposed method under some control conditions. It is shown that our iteration method converges faster than Noor iteration. Moreover, we give some numerical example for comparing the rate of convergence between the Noor iteration and our iteration.
Copyright © 2018 Somchai Kosol. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Cite this article
S. Kosol, Strong convergence theorem of a new iterative method for weak contractions and comparison of the rate of convergence in Banach space, Adv. Fixed Point Theory 8 (2018), 303–312. https://doi.org/10.28919/afpt/3741
BibTeX
@article{Kosol2018,
author = {Kosol, Somchai},
title = {Strong convergence theorem of a new iterative method for weak contractions and comparison of the rate of convergence in Banach space},
journal = {Adv. Fixed Point Theory},
volume = {8},
year = {2018},
pages = {303--312},
doi = {10.28919/afpt/3741}
}