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Nonlinear Fredholm integral equations and majorant functions

  • J. A. EzquerroEmail author
  • M. A. Hernández-Verón
Original Paper
  • 3 Downloads

Abstract

From the majorant principle of Kantorovich and the theoretical significance of Newton’s method, we obtain domains of existence and uniqueness of solution for nonlinear Fredholm integral equations, so that these domains are defined from the positive real zeros of a scalar function that we call majorant function. We illustrate this study with three Fredholm integral equations, where separable and nonseparable kernels are involved, by obtaining domains of existence and uniqueness of solution, approximating solutions numerically and giving a priori and a posteriori error estimates of the approximations.

Keywords

Fredholm integral equation Newton’s method Majorant function Domain of existence of solution Domain of uniqueness of solution Error estimates 

Mathematics Subject Classification (2010)

45G10 47H99 65J15 

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Notes

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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Mathematics and ComputationUniversity of La RiojaLogroñoSpain

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