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On the Local Convergence of a Sixth-Order Iterative Scheme in Banach Spaces

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New Trends in Applied Analysis and Computational Mathematics

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 1356))

Abstract

Applying the Lipschitz continuity of the first-order Fréchet derivative, we describe the local convergence of a sixth-order nonlinear system solver in Banach spaces. This study eliminates the standard practice of Taylor expansion in local analysis and enhances the algorithm applicability through the use of a set of conditions on the first-order derivative. Also, our analysis offers the radii of convergence balls and computable error distances together with the unique result. Various numerical experiments are conducted to demonstrate that our technique is beneficial when prior studies fail to solve problems.

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Acknowledgements

This research is financially supported by the University Grants Commission of India (Ref. No.: 988/(CSIR-UGC NET JUNE 2017); ID: NOV2017-402662).

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Authors and Affiliations

  1. Department of Mathematics, International Institute of Information Technology Bhubaneswar, Bhubaneswar, Odisha, India

    Sanjaya Kumar Parhi & Debasis Sharma

Authors
  1. Sanjaya Kumar Parhi
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  2. Debasis Sharma
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Corresponding author

Correspondence to Sanjaya Kumar Parhi .

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Editors and Affiliations

  1. Department of Mathematics, Veer Surendra Sai University of Technology, Burla, Odisha, India

    Susanta Kumar Paikray

  2. Department of Mathematics, Gauhati University, Guwahati, India

    Hemen Dutta

  3. Department of Mathematics, Center for Mathematics of Uncertainty, Creighton University, Omaha, NE, USA

    John N. Mordeson

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Parhi, S.K., Sharma, D. (2021). On the Local Convergence of a Sixth-Order Iterative Scheme in Banach Spaces. In: Paikray, S.K., Dutta, H., Mordeson, J.N. (eds) New Trends in Applied Analysis and Computational Mathematics. Advances in Intelligent Systems and Computing, vol 1356. Springer, Singapore. https://doi.org/10.1007/978-981-16-1402-6_7

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