Hassan Khandani - Department of Mathematics, Faculty of Science, Mahabad Branch, Islamic Azad university, P.O.Box ۵۹۱۳۵۴۳۳, Mahabad, Iran.
Farshid Khojasteh - Department of Mathematics, Faculty of Science, Arak Branch, Islamic Azad university, Arak, Iran.

We study the convergence of the Krasnoselskii sequence x_{n+۱}=\frac{x_n+g(x_n)}{۲} for non-self mappings on closed intervals. We show that if g satisfies g^{'}\ge -۱ 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.

Krasnoselskii's theorem, Iterative sequence, Newton-Raphson method, Root estimation, Real function