Inexact Newton method under weak and center-weak Lipschitz conditions

Volume 40 / 2013

I. K. Argyros, S. K. Khattri Applicationes Mathematicae 40 (2013), 237-258 MSC: 65H10, 65G99, 47H99, 49H15. DOI: 10.4064/am40-2-6


The paper develops semilocal convergence of Inexact Newton Method INM for approximating solutions of nonlinear equations in Banach space setting. We employ weak Lipschitz and center-weak Lipschitz conditions to perform the error analysis. The results obtained compare favorably with earlier ones in at least the case of Newton's Method (NM). Numerical examples, where our convergence criteria are satisfied but the earlier ones are not, are also explored.


  • I. K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505-6377, U.S.A.
  • S. K. KhattriDepartment of Engineering
    Stord/Haugesund University College
    N-414 Stord, Norway

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