TY - JOUR
ID - 697940
TI - The Krasnoselskii's Method for Real Differentiable Functions
JO - Sahand Communications in Mathematical Analysis
JA - SCMA
LA - en
SN - 2322-5807
AU - Khandani, Hassan
AU - Khojasteh, Farshid
AD - Department of Mathematics, Faculty of Science, Mahabad Branch, Islamic Azad university, P.O.Box 59135433, Mahabad, Iran.
AD - Department of Mathematics, Faculty of Science, Arak Branch, Islamic Azad university, Arak, Iran.
Y1 - 2023
PY - 2023
VL - 20
IS - 1
SP - 95
EP - 106
KW - Krasnoselskii's theorem
KW - Iterative sequence
KW - Newton-Raphson method
KW - Root estimation
KW - Real function
DO - 10.22130/scma.2022.558164.1154
N2 - 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.
UR - https://scma.maragheh.ac.ir/article_697940.html
L1 - https://scma.maragheh.ac.ir/article_697940_b631cdd07cb8d7c4a7e452302e843667.pdf
ER -