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Extending the applicability and convergence domain of a higher-order iterative algorithm under \(\omega \) condition

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Abstract

The main contribution of this study is that the applicability and convergence domain of a fifth-order convergent equation solver is extended. We use \(\omega \) 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. Also, we avoid the use of the extra assumption on boundedness of the first derivative of the nonlinear operator. Our idea can be used on other iterative methods. Numerical tests confirmed that the proposed analysis produces a larger convergence domain, in comparison to the earlier study, without using additional conditions.

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Funding

The second author is funded by University Grants Commission of India (Grant number NOV2017-402662).

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Authors and Affiliations

  1. Department of Mathematical Sciences, Cameron University, Lawton, OK, 73505, USA

    Ioannis K. Argyros

  2. Department of Mathematics, IIIT Bhubaneswar, Bhubaneswar, Odisha, 751003, India

    Debasis Sharma & Shanta Kumari Sunanda

  3. Department of Computer Science, University of Oklahoma, Norman, OK, 73071, USA

    Christopher I. Argyros

  4. Department of Mathematics, Fakir Mohan University, Balasore, Odisha, 756020, India

    Sanjaya Kumar Parhi

Authors
  1. Ioannis K. Argyros
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  2. Debasis Sharma
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  3. Christopher I. Argyros
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  4. Sanjaya Kumar Parhi
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  5. Shanta Kumari Sunanda
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Correspondence to Debasis Sharma.

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Argyros, I.K., Sharma, D., Argyros, C.I. et al. Extending the applicability and convergence domain of a higher-order iterative algorithm under \(\omega \) condition. Rend. Circ. Mat. Palermo, II. Ser 71, 469–482 (2022). https://doi.org/10.1007/s12215-021-00624-8

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  • DOI: https://doi.org/10.1007/s12215-021-00624-8

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