Convergence analysis of the Picard–Ishikawa hybrid iterative process with applications

The purpose of this paper is to introduce the Picard–Ishikawa hybrid iterative process. This new iterative process can be seen as a hybrid of Picard and Ishikawa iterative processes. It is our purpose in this paper to show that this new hybrid iterative process converges faster than all of Picard, Krasnoselskii, Mann, Ishikawa, Noor, Picard–Mann and Picard–Krasnoselskii iterative processes in the sense of Berinde (Iterative Approximation of Fixed Points. Efemeride, Baia Mare, 2002). We establish data dependence and stability results for our newly developed iterative process. Moreover, we apply our newly developed iterative process in finding the solution of delay differential equations.