On an iterative method without inverses of derivatives for solving equations

Open Access

Original research article

Author(s):

Ioannis K. Argyros^a, Santhosh George^b

^aDepartment of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
^bDepartment of Mathematical and Computational Sciences, National Institute of Technology Karnataka, India

Advances in the Theory of Nonlinear Analysis and its Applications 4(2), 67-76.

Received: September 26, 2019

Accepted: February 21, 2020

Published: March 13, 2020

Abstract

We present the semi-local convergence analysis of a Potra-type method to solve equations involving Banach space-valued operators. The analysis is based on our ideas of recurrent functions and restricted convergence regions. The study is supported with numerical examples.

Keywords: Multi-step method, local convergence, Fréchet derivative, system of equations, Banach space.

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APA Style

George, S., & Argyros, İ. K. (2020). On an iterative method without inverses of derivatives for solving equations. Advances in the Theory of Nonlinear Analysis and its Application, 4(2), 67-76.