Comparison of the Rate of Convergence of Various Iterative Methods for the Class of Weak Contractions in Banach Spaces

Withun Phuengrattana, Suthep Suantai

Abstract

In this article, we propose a new iterative method for finding fixed points of a class of weak contractions in arbitrary Banach spaces. Comparison of the rate of convergence between Mann, Ishikawa, Noor iterations, and the proposed iterative method are also discussed. It is shown that the proposed iterative method converges faster than the others. Moreover, we give a numerical example for comparing the rate of convergence of those methods.