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Expanding the applicability of a fifth-order convergent method in a Banach space under weak conditions

Volume 45 / 2018

Ioannis K. Argyros, Ramandeep Behl, S. S. Motsa Applicationes Mathematicae 45 (2018), 91-101 MSC: 65G99, 65H10, 47J25, 47J05. DOI: 10.4064/am2303-11-2016 Published online: 28 May 2018

Abstract

We present a local convergence analysis for a fifth-order convergent method in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In contrast to the earlier studies using hypotheses up to the fifth Fréchet derivative, we only use hypotheses on the first-order Fréchet derivative and Lipschitz constants. In this way, we not only expand the applicability of the methods but also evaluate the theoretical radius of convergence of these methods. Finally, a variety of concrete numerical examples demonstrate that our results even apply to solve those nonlinear equations where earlier studies cannot apply.

Authors

  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
    e-mail
  • Ramandeep BehlDepartment of Mathematics
    King Abdulaziz University
    Jeddah 21589, Saudi Arabia
    e-mail
  • S. S. MotsaSchool of Mathematics, Statistics and Computer Science
    University of KwaZulu-Natal
    Private Bag X01, Scottsville 3209
    Pietermaritzburg, South Africa
    e-mail

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