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

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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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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Keywords

  • Fréchet derivative
  • Order of convergence
  • Iterative method
  • Banach space

Mathematics Subject Classification

  • 65G49
  • 47H99