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Newton–Kantorovich regularization method for nonlinear ill-posed equations involving \(m-\)accretive operators in Banach spaces

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Abstract

In this paper, we study nonlinear ill-posed problems involving \(m-\)accretive mappings in Banach spaces. We consider Newton–Kantorovich regularization method for the implementation of Lavrentiev regularization method. Using general Hölder type source condition we obtain an error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060–2076, 2005) for choosing the regularization parameter.

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Acknowledgements

Sreedeep would like to thank National Institute of Technology Karnataka, India, for the financial support.

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Authors and Affiliations

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

    C. D. Sreedeep & Santhosh George

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

    Ioannis K. Argyros

Authors
  1. C. D. Sreedeep
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  2. Santhosh George
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  3. Ioannis K. Argyros
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Correspondence to Santhosh George.

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Sreedeep, C.D., George, S. & Argyros, I.K. Newton–Kantorovich regularization method for nonlinear ill-posed equations involving \(m-\)accretive operators in Banach spaces. Rend. Circ. Mat. Palermo, II. Ser 69, 459–473 (2020). https://doi.org/10.1007/s12215-019-00413-4

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