A Unified Convergence Analysis for Some Two-Point Type Methods for Nonsmooth Operators

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URI: http://hdl.handle.net/10317/9443
ISSN: 2227-7390
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Author
Amat Plata, Sergio; Argyros, Ioannis; Busquier Sáez, Sonia; Hernández Verón, Miguel Ángel; Rubio, María Jesús
Knowledge Area
Matemática Aplicada
Sponsors
Research of the first and third authors supported in part by Programa de Apoyo a la investigación de la fundación Séneca-Agencia de Ciencia y Tecnología de la Región de Murcia 20928/PI/18 and by MTM2015-64382-P. Research of the fourth and fifth authors supported by Ministerio de Economía y Competitividad under grant MTM2014-52016-C2-1P. This research received no external funding.
Realizado en/con
Universidad de la Rioja
Publication date
2019-08-03
Publisher
MDPI
Bibliographic Citation
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
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Si
Keywords
Iterative methods
Nonlinear equations
Newton-type methods
Smooth and nonsmooth operators
Abstract
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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