Extensions of Kantorovich-type theorems for Newton’s method

Ioannis K. Argyros, Santhosh George, Daya Ram Sahu Applicationes Mathematicae MSC: 65G99, 47H17, 49M15. DOI: 10.4064/am2352-1-2018 Opublikowany online: 7 June 2019


We extend the applicability of Newton’s method, so we can approximate a locally unique solution of a nonlinear equation in a Banach space setting in cases not covered before. To achieve this, we find a more precise set containing the Newton iterates than in earlier works.


  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
  • Santhosh GeorgeDepartment of Mathematical and
    Computational Sciences
    National Institute of Technology
    Karnataka, India
  • Daya Ram SahuDepartment of Mathematics
    Banaras Hindu University
    Varanasi 221005, India

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