Extending the Applicability and Convergence Domain of a Fifth-Order Iterative Scheme under Hölder Continuous Derivative in Banach Spaces

Authors

  • Debasis Sharma Department of Mathematics, IIIT Bhubaneswar, Odisha, India https://orcid.org/0000-0001-8456-6391
  • Sanjaya Kumar Parhi Department of Mathematics, Fakir Mohan University, Odisha, India
  • Shanta Kumari Sunanda Department of Mathematics, IIIT Bhubaneswar, Odisha, India

DOI:

https://doi.org/10.37256/cm.242021962

Keywords:

iterative schemes, Banach space, local convergence, Hölder continuity condition

Abstract

The most significant contribution made by this study is that the applicability and convergence domain of a fifth-order convergent nonlinear equation solver is extended. We use Hölder condition on the first Fréchet derivative to study the local analysis, and this expands the applicability of the formula for such problems where the earlier study based on Lipschitz constants cannot be used. This study generalizes the local analysis based on Lipschitz constants. Also, we avoid the use of the extra assumption on boundedness of the first derivative of the involved operator. Finally, numerical experiments ensure that our analysis expands the utility of the considered scheme. In addition, the proposed technique produces a larger convergence domain, in comparison to the earlier study, without using any extra conditions.

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Published

2021-09-06

How to Cite

1.
Sharma D, Parhi SK, Sunanda SK. Extending the Applicability and Convergence Domain of a Fifth-Order Iterative Scheme under Hölder Continuous Derivative in Banach Spaces. Contemp. Math. [Internet]. 2021 Sep. 6 [cited 2024 Jul. 18];2(4):258-70. Available from: https://ojs.wiserpub.com/index.php/CM/article/view/962