Nth Composite Iterative Scheme via Weak Contractions with Application

Abstract

The main goal of this study is to formulate an effective iterative scheme, namely, an $n^{\mathrm{t}\mathrm{h}}-$ composite iterative scheme for approximating the fixed point of a self-map $T:\mathcal{U}⟶\mathcal{U}$ with weak contraction property. We show that the $n^{\mathrm{t}\mathrm{h}}-$ composite iterative scheme is faster than the scheme obtained by Sintunavarat–Pitea’s iterative scheme. We present some examples using the MATLAB simulator to illustrate our results. Finally, we approximate the solution of some integral equations using our scheme and the Sintunavarat–Pitea scheme.