In this paper, we introduce an iteration process to approximate a fixed
point of a contractive self-mapping. The comparison theorem indicates
that our iteration process is faster than the other existing iteration
processes in the literature. We also obtain convergence and stability
theorems of this iterative process for a contractive self-mapping.
Numerical examples show that our iteration process for approximating a
fixed point of a contractive self-mapping is faster than the existing
methods. Based on this process, we finally present a new modified
Newton-Raphson method for finding the roots of a function and generate
some nice polynomiographs.