University of MaraghehSahand Communications in Mathematical Analysis2322-580720120230101The Krasnoselskii's Method for Real Differentiable Functions9510669794010.22130/scma.2022.558164.1154ENHassanKhandaniDepartment of Mathematics, Faculty of Science, Mahabad Branch, Islamic Azad university, P.O.Box 59135433, Mahabad, Iran.0000-0002-77748335FarshidKhojastehDepartment of Mathematics, Faculty of Science, Arak Branch, Islamic Azad university, Arak, Iran.Journal Article20220720We 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.https://scma.maragheh.ac.ir/article_697940_b631cdd07cb8d7c4a7e452302e843667.pdf