A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators
1
Departamentode Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 11003 Cádiz, Spain
2
Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
3
Departamento de Matemáticas y Computación, Universidad de La Rioja, Calle Madre de Dios, 53, 26006 Logrono, Spain
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Mathematics 2019, 7(8), 701; https://doi.org/10.3390/math7080701
Received: 18 June 2019
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Revised: 31 July 2019
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Accepted: 31 July 2019
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Published: 3 August 2019
(This article belongs to the Special Issue Iterative Methods for Solving Nonlinear Equations and Systems)
The aim of this paper is the approximation of nonlinear equations using iterative methods. We present a unified convergence analysis for some two-point type methods. This way we compare specializations of our method using not necessarily the same convergence criteria. We consider both semilocal and local analysis. In the first one, the hypotheses are imposed on the initial guess and in the second on the solution. The results can be applied for smooth and nonsmooth operators.
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Keywords:
iterative methods; nonlinear equations; Newton-type methods; smooth and nonsmooth operators
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited
MDPI and ACS Style
Amat, S.; Argyros, I.; Busquier, S.; Hernández-Verón, M.Á.; Rubio, M.J. A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators. Mathematics 2019, 7, 701. https://doi.org/10.3390/math7080701
AMA Style
Amat S, Argyros I, Busquier S, Hernández-Verón MÁ, Rubio MJ. A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators. Mathematics. 2019; 7(8):701. https://doi.org/10.3390/math7080701
Chicago/Turabian StyleAmat, Sergio, Ioannis Argyros, Sonia Busquier, Miguel Á. Hernández-Verón, and María J. Rubio. 2019. "A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators" Mathematics 7, no. 8: 701. https://doi.org/10.3390/math7080701
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