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Algorithms 2017, 10(3), 89; https://doi.org/10.3390/a10030089

On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique

Department of Mathematics and Computation, University of La Rioja, C/ Madre de Dios, 53, 26006 Logroño, Spain
These authors contributed equally to this work.
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Received: 16 May 2017 / Revised: 13 July 2017 / Accepted: 30 July 2017 / Published: 2 August 2017
(This article belongs to the Special Issue Numerical Algorithms for Solving Nonlinear Equations and Systems 2017)
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Abstract

The well-known Kantorovich technique based on majorizing sequences is used to analyse the convergence of Newton’s method when it is used to solve nonlinear Fredholm integral equations. In addition, we obtain information about the domains of existence and uniqueness of a solution for these equations. Finally, we illustrate the above with two particular Fredholm integral equations. View Full-Text
Keywords: Fredholm integral equation; Newton’s method; convergence; Kantorovich’s technique; domain of existence of a solution; domain of uniqueness of a solution. Fredholm integral equation; Newton’s method; convergence; Kantorovich’s technique; domain of existence of a solution; domain of uniqueness of a solution.
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. (CC BY 4.0).
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Ezquerro, J.A.; Hernández-Verón, M.Á. On the Existence of Solutions of Nonlinear Fredholm Integral Equations from Kantorovich’s Technique. Algorithms 2017, 10, 89.

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