The aim of this paper is to define a new iteration scheme Nv1 which converges to a fixed point faster than some previously existing methods such as Picard, Mann, Ishikawa, Noor, SP, CR, S, Picard-S, Garodia, K and K∗ methods etc. The effectiveness and efficiency of our algorithm is confirmed by numerical example and some strong convergence, weak convergence, T-stability and data dependence results for contraction mapping are also proven. Moreover, it is shown that differential equation with retarted argument is solved using Nv1 iteration process. © 2020 EJPAM. All rights reserved.