Computational Mathematics and Computer Modeling with Applications (CMCMA)

On the semi-local convergence of the Homeier method in Banach space for solving equations

https://doi.org/10.52547/CMCMA.1.1.63
Volume 1, Issue 1 - Serial Number 1
June 2022
Pages 63-68
Computational Mathematics and Computer Modeling with Applications (CMCMA)

Document Type : Invited paper

Authors

Samundra Regmi 1
Ioannis Konstantinos Argyros 2
Santhosh George 3
Christopher I. Argyros 4

1 Learning Commons, University of North Texas at Dallas, Dallas, TX, USA

2 Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA

3 Department of Mathematical and Computational Sciences,National Institute of Technology Karnataka, India-575 025

4 Department of Computing and Technology, Cameron University, Lawton, OK 73505, USA

Abstract
In this paper we consider the semi-local convergence analysis of the Homeier method for solving nonlinear equation in Banach space. As far as we know no semi-local convergence has been given for the Homeier under Lipschitz conditions. Our goal is to extend the applicability of the Homeier method in the semi-local convergence under these conditions. We use majorizing sequences and conditions only on the first derivative which appear on the method for proving our results. Numerical experiments are provided in this study.

Keywords

semi-local convergence
Homeier method
iterative methods
Banach space
convergence criterion
  • Receive Date 15 February 2022
  • Accept Date 18 March 2022

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