Ball convergence theorems for Maheshwari-type eighth-order methods under weak conditions

Abstract

We present a local convergence analysis for a family of Maheshwari-type eighth-order methods in order to approximate a solution of a nonlinear equation. We use hypotheses up to the first derivative in contrast to earlier studies such as Cordero et al. (J Comput Appl Math 291(1):348–357, 2016), Maheshwari (Appl Math Comput 211:283–391, 2009), Petkovic et al. (Multipoint methods for solving nonlinear equations. Elsevier, Amsterdam, 2013) using hypotheses up to the seventh derivative. This way the applicability of these methods is extended under weaker hypotheses. Moreover the radius of convergence and computable error bounds on the distances involved are also given in this study. Numerical examples are also presented in this study. © 2015, Instituto de Matemática e Estatística da Universidade de São Paulo.