Local convergence for a Chebyshev-type method in Banach space free of derivatives – Advances in the theory of nonlinear analysis and its applications

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Original research article

Local convergence for a Chebyshev-type method in Banach space free of derivatives\

Author(s):

Ioannis K. Argyros^a, Santhosh George^b

^a Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
^b Department of Mathematical and Computational Sciences, National Institute of Technology, Karnataka, 575 025, India

Advances in the Theory of Nonlinear Analysis and its Applications 2(1), 62-69.

Received: March 2, 2018

Accepted: March 25, 2018

Published: March 28, 2018

Abstract

This paper is devoted to the study of a Chebyshev-type method free of derivatives for solving nonlinear equations in Banach spaces. Using the idea of restricted convergence domain, we extended the applicability of the Chebyshev-type methods. Our convergence conditions are weaker than the conditions used in earlier studies. Therefore, the applicability of the method is extended. Numerical examples where earlier results cannot apply to solve equations but our results can apply are also given in this study.

Keywords: Chebyshev-type method, restricted convergence domain, radius of convergence, local convergence.

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APA Style

George, S., & Argyros, I. K. (2018). Local convergence for a Chebyshev-type method in Banach space free of derivatives. Advances in the Theory of Nonlinear Analysis and its Application, 2(1), 62-69.