Strong convergence theorem of a new iterative method for weak contractions and comparison of the rate of convergence in Banach space

Abstract

In this paper, we first construct a new iteration method for approximating fixed points of a class of weak contractions in a Banach space and then prove strong convergence theorem of the proposed method under some control conditions. It is shown that our iteration method converges faster than Noor iteration. Moreover, we give some numerical example for comparing the rate of convergence between the Noor iteration and our iteration.