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A note on “Convergence radius of Osada’s method under Hölder continuous condition”

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  • Hueso, José L.
  • Martínez, Eulalia
  • Gupta, D.K.
  • Cevallos, Fabricio

Abstract

In this paper we revise the proofs of the results obtained in “Convergence radius of Osada’s method under Hölder continuous condition” [4], because the remainder of the Taylor’s expansion used for the obtainment of the local convergence radius is not correct. So we perform the complete study in order to modify the equation for getting the local convergence radius, the uniqueness radius and the error bounds. Moreover a dynamical study for the third order Osada’s method is also developed.

Suggested Citation

  • Hueso, José L. & Martínez, Eulalia & Gupta, D.K. & Cevallos, Fabricio, 2018. "A note on “Convergence radius of Osada’s method under Hölder continuous condition”," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 689-699.
    • Handle: RePEc:eee:apmaco:v:321:y:2018:i:c:p:689-699
    DOI: 10.1016/j.amc.2017.11.003
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    References listed on IDEAS

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    1. Liu, Suzhen & Song, Yongzhong & Zhou, Xiaojian, 2015. "Convergence radius of Halley’s method for multiple roots under center-Hölder continuous condition," Applied Mathematics and Computation, Elsevier, vol. 265(C), pages 1011-1018.
    2. Argyros, Ioannis K. & Magreñán, Á. Alberto, 2015. "On the convergence of an optimal fourth-order family of methods and its dynamics," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 336-346.
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