Expanding the applicability of two-point Newton-like methods under generalized conditions

Volume 40 / 2013

Ioannis K. Argyros, Saïd Hilout Applicationes Mathematicae 40 (2013), 63-90 MSC: 65J15, 65G99, 47H99, 49M15. DOI: 10.4064/am40-1-4


We use a two-point Newton-like method to approximate a locally unique solution of a nonlinear equation containing a non-differentiable term in a Banach space setting. Using more precise majorizing sequences than in earlier studies, we present a tighter semi-local and local convergence analysis and weaker convergence criteria. This way we expand the applicability of these methods. Numerical examples are provided where the old convergence criteria do not hold but the new convergence criteria are satisfied.


  • Ioannis K. ArgyrosCameron University
    Department of Mathematical Sciences
    Lawton, OK 73505, U.S.A.
  • Saïd HiloutPoitiers University
    Laboratoire de Mathématiques et Applications
    Bd. Pierre et Marie Curie
    Téléport 2, B.P. 30179
    86962 Futuroscope Chasseneuil Cedex, France

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