# Extended Higher Order Iterative Method for Nonlinear Equations and its Convergence Analysis in Banach Spaces

## Authors

• Gagan Deep Department of Mathematics, Hans Raj Mahila Mahavidyalaya, Jalandhar, Punjab, India
• Ioannis K. Argyros Department of Computing and Mathematical Sciences, Cameron University, Lawton, USA
• Gaurav Verma Department of Mathematics, Hans Raj Mahila Mahavidyalaya, Jalandhar, Punjab, India https://orcid.org/0000-0002-6748-0796
• Simardeep Kaur Department of Mathematics, Hans Raj Mahila Mahavidyalaya, Jalandhar, Punjab, India
• Rajdeep Kaur Department of Mathematics, Hans Raj Mahila Mahavidyalaya, Jalandhar, Punjab, India
• Samundra Regmi Department of Mathematics, University of Houston, Houston, USA

## Keywords:

nonlinear equations, Newton’s method, order of convergence, error analysis, banach space, convergence

## Abstract

In this article, a novel higher order iterative method for solving nonlinear equations is developed. The new iterative method obtained from fifth order Newton-Özban method attains eighth order of convergence by adding a single step with only one additional function evaluation. The method is extended to Banach spaces and its local as well as semi-local convergence analysis is done under generalized continuity conditions. The existence and uniqueness results of solution are also provided along with radii of convergence balls. From the numerical experiments, it can be inferred that the proposed method is more accurate and effective in high precision computations than existing eighth order methods. The computation of error analysis and norm of functions demonstrate that proposed method takes a lead over the considered methods.

2024-01-08

## How to Cite

1.
Deep G, Argyros IK, Verma G, Kaur S, Kaur R, Regmi S. Extended Higher Order Iterative Method for Nonlinear Equations and its Convergence Analysis in Banach Spaces. Contemp. Math. [Internet]. 2024 Jan. 8 [cited 2024 Jun. 17];5(1):230-54. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/3866

Research Article