Extended Newton-type iteration for nonlinear ill-posed equations in Banach space

  • C. D. SreedeepEmail author
  • Santhosh George
  • Ioannis K. Argyros
Original Research


In this paper, we study nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. We produce an extended Newton-type iterative scheme that converges cubically to the solution which uses assumptions only on the first Fréchet derivative of the operator. 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.


Extended Newton iterative scheme Nonlinear ill-posed problem Banach space Lavrentiev regularization m-Accretive mappings Adaptive parameter choice strategy 

Mathematics Subject Classification

47J06 47J05 65J20 47H06 49J30 



The work of Santhosh George is supported by the Core Research Grant by SERB, Department of Science and Technology, Govt. of India, EMR/2017/001594. Sreedeep would like to thank National Institute of Technology Karnataka, India, for the financial support.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2018

Authors and Affiliations

  • C. D. Sreedeep
    • 1
    Email author
  • Santhosh George
    • 1
  • Ioannis K. Argyros
    • 2
  1. 1.Department of Mathematical and Computational SciencesNational Institute of Technology KarnatakaMangaluruIndia
  2. 2.Department of Mathematical SciencesCameron UniversityLawtonUSA

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