New four step iteration process for approximating fixed point of contraction mappings

Abstract

This paper introduces a new iteration process for the approximation of fixed points of contraction mapping. We prove the comparison theorem to indicate that our iteration process converges faster than the other iteration processes and also prove data dependence, stability, and convergence results. Moreover, we give numerical examples to check the performance of our algorithm over the Piri, SM, CR, and $K^*$ iterations process for different types of functions.