On the convergence of secant-like algorithms with applications to generalized fractional calculus

Volume 43 / 2016

George A. Anastassiou, Ioannis K. Argyros Applicationes Mathematicae 43 (2016), 191-206 MSC: 65G99, 65H10, 26A33, 47J25, 47J05. DOI: 10.4064/am2275-12-2015 Published online: 10 December 2015

Abstract

We present local and semilocal convergence results for secant-like algorithms in order to approximate a locally unique solution of a nonlinear equation in a Banach space setting. In the last part of the study we present some choices of the operators involved in fractional calculus where the operators satisfy the convergence conditions.

Authors

  • George A. AnastassiouDepartment of Mathematical Sciences
    University of Memphis
    Memphis, TN 38152, U.S.A.
    e-mail
  • Ioannis K. ArgyrosDepartment of Mathematical Sciences
    Cameron University
    Lawton, OK 73505, U.S.A.
    e-mail

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