Rapid Convergence of New FP Iterative Algorithm

In this paper, a new iterative process called NIP is introduced and some convergence theorems for approximation of fixed points (FPs) of contractive and non-expansive maps are proved. It is also shown that NIP converges rapidly than many existing iterative processes. This new iterative scheme requires least number of iterations as compared with the existing iteration procedures like Picard, Mann, Ishikawa, Noor, Agarwal, Abbas and many others. Further, the same is validated numerically as well as graphically by considering some standard functions.