%0 Journal Article
%T The Krasnoselskii's Method for Real Differentiable Functions
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Khandani, Hassan
%A Khojasteh, Farshid
%D 2023
%\ 01/01/2023
%V 20
%N 1
%P 95-106
%! The Krasnoselskii's Method for Real Differentiable Functions
%K Krasnoselskii's theorem
%K Iterative sequence
%K Newton-Raphson method
%K Root estimation
%K Real function
%R 10.22130/scma.2022.558164.1154
%X 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.
%U https://scma.maragheh.ac.ir/article_697940_b631cdd07cb8d7c4a7e452302e843667.pdf