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 -