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Local convergence for a multi-point family of super-Halley methods in a Banach space under weak conditions

Volume 42 / 2015

Ioannis K. Argyros, Santhosh George Applicationes Mathematicae 42 (2015), 193-203 MSC: 65D10, 65D99. DOI: 10.4064/am42-2-6


We present a local multi-point convergence analysis for a family of super-Halley methods of high convergence order in order to approximate a solution of a nonlinear equation in a Banach space. Our sufficient convergence conditions involve only hypotheses on the first and second Fréchet derivative of the operator involved. Earlier studies use hypotheses up to the third Fréchet derivative. Numerical examples are also provided.


  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
  • Santhosh GeorgeDepartment of Mathematical
    and Computational Sciences
    National Institute of Technology
    Karnataka, India 757 025

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