Extensions of Kantorovich-type theorems for Newton’s method

Volume 47 / 2020

Ioannis K. Argyros, Santhosh George, Daya Ram Sahu Applicationes Mathematicae 47 (2020), 145-153 MSC: 65G99, 47H17, 49M15. DOI: 10.4064/am2352-1-2018 Published online: 7 June 2019

Abstract

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.

Authors

  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
    ORCID: 0000-0003-1609-3195
    e-mail
  • Santhosh GeorgeDepartment of Mathematical and
    Computational Sciences
    National Institute of Technology
    Karnataka, India
    ORCID: 0000-0002-3530-5539
    e-mail
  • Daya Ram SahuDepartment of Mathematics
    Banaras Hindu University
    Varanasi 221005, India
    e-mail

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