Improved ball convergence of Newton's method under general conditions

Tom 39 / 2012

Ioannis K. Argyros, Hongmin Ren Applicationes Mathematicae 39 (2012), 365-375 MSC: 65G99, 65K10, 47H17, 49M15, 90C30 DOI: 10.4064/am39-3-9


We present ball convergence results for Newton's method in order to approximate a locally unique solution of a nonlinear operator equation in a Banach space setting. Our hypotheses involve very general majorants on the Fréchet derivatives of the operators involved. In the special case of convex majorants our results, compared with earlier ones, have at least as large radius of convergence, no less tight error bounds on the distances involved, and no less precise information on the uniqueness of the solution.


  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
  • Hongmin RenCollege of Information and Electronics
    Hangzhou Polytechnic
    Hangzhou 311402, Zhejiang, P.R. China

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