Document Type : Research Paper


1 Department of Mathematics, Faculty of Science, Mahabad Branch, Islamic Azad university, P.O.Box 59135433, Mahabad, Iran.

2 Department of Mathematics, Faculty of Science, Arak Branch, Islamic Azad university, Arak, Iran.


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.


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