Convergence of Chun’s method in Banach spaces under weaker assumptions

Abstract

In this paper, we give a modified convergence analysis for the fourth-order method studied in Cordero et al. (J Math Chem 53(1):430–449, 2015). Our analysis provides the convergence order using the derivative of the involved operator up to order two only, whereas their study needs it to be five times differentiable. Apart from this, this paper obtains the convergence ball radius and the number of iterations to reach the solution with the desired accuracy. Further, we use the general Banach space settings to get these results, while their work is done only for the space. At the end of the paper, we discuss a few numerical examples and compare them with other existing fourth-order methods. © The Author(s), under exclusive licence to The Forum D’Analystes 2025.