Newton's methods for variational inclusions under conditioned Fréchet derivative

Volume 34 / 2007

Ioannis K. Argyros, Saïd Hilout Applicationes Mathematicae 34 (2007), 349-357 MSC: 47H04, 65K10, 49J53. DOI: 10.4064/am34-3-6

Abstract

Estimates of the radius of convergence of Newton's methods for variational inclusions in Banach spaces are investigated under a weak Lipschitz condition on the first Fréchet derivative. We establish the linear convergence of Newton's and of a variant of Newton methods using the concepts of pseudo-Lipschitz set-valued map and $\omega $-conditioned Fréchet derivative or the center-Lipschitz condition introduced by the first author.

Authors

  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
    e-mail
  • Saïd HiloutDepartment of Applied Mathematics
    and Computation
    Faculty of Science and Technics of Béni-Mellal
    B.P. 523, Béni-Mellal 23000, Morocco
    e-mail

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