On some extensions of Banach's contraction principle and applications to the convergence and stability of some iterative processes
Abstract
In this paper, we obtain existence and uniqueness results of fixed points of nonlinear operators satisfying the condition of the form (Φ1,Φ2) given as a perturbation of Φ2 contraction by a convenable function Φ1 in metric and Banach spaces, which enable us to extend the Banach’s mapping principle and other results in the literature. Also, the Φ-quasi nonexpansive character of our context is shown in order to obtain results of convergence and stability of iterative processes of Mann and Ishikawa.
Copyright © 2014 Nadjeh Redjel. 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
N. Redjel, On some extensions of Banach's contraction principle and applications to the convergence and stability of some iterative processes, Adv. Fixed Point Theory 4 (2014), 555–570.
BibTeX
@article{Redjel2014,
author = {Redjel, Nadjeh},
title = {On some extensions of Banach's contraction principle and applications to the convergence and stability of some iterative processes},
journal = {Adv. Fixed Point Theory},
volume = {4},
year = {2014},
pages = {555--570},
doi = {}
}