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Convergence Analysis of a Fifth-Order Iterative Method Using Recurrence Relations and Conditions on the First Derivative

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Abstract

Using conditions on the second Fréchet derivative, fifth order of convergence was established in Singh et al. (Mediterr J Math 13:4219–4235, 2016) for an iterative method. In this paper, we establish fifth order of convergence of the method using assumptions only on the first Fréchet derivative of the involved operator.

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Acknowledgements

The works of Santhosh George and Jidesh P are supported by the Core Research Grant by SERB, Department of Science and Technology, Govt. of India, EMR/2017/001594.

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Authors and Affiliations

  1. Department of Mathematical and Computational Sciences, National Institute of Technology Karnataka, Mangaluru, 575 025, India

    S. George, P. Jidesh, M. Mahapatra & M. Saeed

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

    I. K. Argyros

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  1. S. George
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  2. I. K. Argyros
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  3. P. Jidesh
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  4. M. Mahapatra
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  5. M. Saeed
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Correspondence to S. George.

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George, S., Argyros, I.K., Jidesh, P. et al. Convergence Analysis of a Fifth-Order Iterative Method Using Recurrence Relations and Conditions on the First Derivative. Mediterr. J. Math. 18, 57 (2021). https://doi.org/10.1007/s00009-021-01697-6

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  • DOI: https://doi.org/10.1007/s00009-021-01697-6

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