A novel iterative scheme for solving delay differential equations and nonlinear integral equations in Banach spaces

Abstract

We propose a three‐step iteration process for finding the common fixed points of nonexpansive mapping and strongly pseudocontractive mapping in a real Banach space. We weaken the necessity of condition (C) imposed by a previous study on the mappings by using a quite simple and different method to obtain strong convergence of our proposed iterative scheme to the common fixed point of nonexpansive mapping and strongly pseudocontractive mapping. Numerically, we also show that our proposed iterative scheme converges faster than some existing iterative schemes. Furthermore, we apply our proposed iterative process in solving mixed type Volterra‐Fredholm functional nonlinear integral equations and delay differential equations.