Title: Local convergence of a fast Steffensen-type method on Banach space under weak conditions

Authors: Ioannis K. Argyros; Santhosh George

Addresses: Department of Mathematical Sciences, Cameron University, Lawton, 73505, OK, USA ' Department of Mathematical and Computational Sciences, NIT Karnataka, 575 025, India

Abstract: This paper is devoted to the study of the seventh-order Steffensen-type methods for solving nonlinear equations in Banach spaces. Using the idea of a restricted convergence domain, we extended the applicability of the seventh-order Steffensen-type methods. Our convergence conditions are weaker than the conditions used in the earlier studies. Numerical examples are also given in this study.

Keywords: Steffensen-type method; restricted convergence domain; radius of convergence; local convergence.

DOI: 10.1504/IJCSM.2017.088975

International Journal of Computing Science and Mathematics, 2017 Vol.8 No.6, pp.495 - 505

Received: 01 Jun 2017
Accepted: 13 Jun 2017

Published online: 03 Jan 2018 *

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