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

Sergio Amat, Ioannis Argyros, Sonia Busquier, Miguel Ángel Hernández-Verón and María Jesús Rubio
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Sergio Amat: Departamentode Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 11003 Cádiz, Spain
Ioannis Argyros: Department of Mathematical Sciences, Cameron University, Lawton, OK 73505, USA
Sonia Busquier: Departamentode Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, 11003 Cádiz, Spain
Miguel Ángel Hernández-Verón: Departamento de Matemáticas y Computación, Universidad de La Rioja, Calle Madre de Dios, 53, 26006 Logrono, Spain
María Jesús Rubio: Departamento de Matemáticas y Computación, Universidad de La Rioja, Calle Madre de Dios, 53, 26006 Logrono, Spain

Mathematics, 2019, vol. 7, issue 8, 1-12

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.

Keywords: iterative methods; nonlinear equations; Newton-type methods; smooth and nonsmooth operators (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2019
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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