On the convergence of the sixth order Homeier like method in Banach spaces

Abstract

A sixth order Homeier-like method is introduced for approximating a solution of the non-linear equation in Banach space. Assumptions only on first and second derivatives are used to obtain a sixth order convergence. Our proof does not depend on Taylor series expansions as in the earlier studies for the similar methods. © 2022, Erdal Karapinar. All rights reserved.