@article {
author = {Khandani, Hassan and Khojasteh, Farshid},
title = {The Krasnoselskii's Method for Real Differentiable Functions},
journal = {Sahand Communications in Mathematical Analysis},
volume = {20},
number = {1},
pages = {95-106},
year = {2023},
publisher = {University of Maragheh},
issn = {2322-5807},
eissn = {2423-3900},
doi = {10.22130/scma.2022.558164.1154},
abstract = {We study the convergence of the Krasnoselskii sequence $x_{n+1}=\frac{x_n+g(x_n)}{2}$ for non-self mappings on closed intervals. We show that if $g$ satisfies $g^{'}\ge -1$ along with some other conditions, this sequence converges to a fixed point of $g$. We extend this fixed-point result to a novel and efficient root-finding method. We present concrete examples at the end. In these examples, we make a comparison between Newton-Raphson and our method. These examples also reveal how our method can be applied efficiently to find the fixed points of a real-valued function.},
keywords = {Krasnoselskii's theorem,Iterative sequence,Newton-Raphson method,Root estimation,Real function},
url = {https://scma.maragheh.ac.ir/article_697940.html},
eprint = {https://scma.maragheh.ac.ir/article_697940_b631cdd07cb8d7c4a7e452302e843667.pdf}
}