scholarly journals How to Obtain Global Convergence Domains via Newton’s Method for Nonlinear Integral Equations

Mathematics ◽  
2019 ◽  
Vol 7 (6) ◽  
pp. 553 ◽  
Author(s):  
José Antonio Ezquerro ◽  
Miguel Ángel Hernández-Verón
Keyword(s):  
Global Convergence ◽  
Integral Equations ◽  
Newton’S Method ◽  
Existence And Uniqueness ◽  
Newton's Method ◽  
Uniqueness Of Solution ◽  
Nonlinear Integral Equations ◽  
Theoretical Significance

We use the theoretical significance of Newton’s method to draw conclusions about the existence and uniqueness of solution of a particular type of nonlinear integral equations of Fredholm. In addition, we obtain a domain of global convergence for Newton’s method.

scholarly journals An application of Newton's method to differential and integral equations

2001 ◽  
Vol 42 (3) ◽  
pp. 372-386 ◽  
Author(s):  
J. M. Gutiérrez ◽  
M. A. Hernández
Keyword(s):  
Integral Equations ◽  
Error Estimates ◽  
Newton’S Method ◽  
Existence And Uniqueness ◽  
Newton's Method ◽  
Uniqueness Of A Solution ◽  
Differential And Integral Equations

AbstractNewton's method is applied to an operator that satisfies stronger conditions than those of Kantorovich. Convergence and error estimates are compared in the two situations. As an application, we obtain information on the existence and uniqueness of a solution for differential and integral equations.

scholarly journals Implicit-Relation-Type Cyclic Contractive Mappings and Applications to Integral Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-15 ◽  
Author(s):  
Hemant Kumar Nashine ◽  
Zoran Kadelburg ◽  
Poom Kumam
Keyword(s):  
Integral Equations ◽  
Existence And Uniqueness ◽  
Contractive Condition ◽  
Uniqueness Of Solutions ◽  
Nonlinear Integral Equations ◽  
Implicit Relation ◽  
Existence And Uniqueness Results ◽  
Contractive Mappings ◽  
Uniqueness Results ◽  
Relation Type

We introduce an implicit-relation-type cyclic contractive condition for a map in a metric space and derive existence and uniqueness results of fixed points for such mappings. Examples are given to support the usability of our results. At the end of the paper, an application to the study of existence and uniqueness of solutions for a class of nonlinear integral equations is presented.

scholarly journals The Newtonian Operator and Global Convergence Balls for Newton’s Method

Mathematics ◽  
2020 ◽  
Vol 8 (7) ◽  
pp. 1074
Author(s):  
José A. Ezquerro ◽  
Miguel A. Hernández-Verón
Keyword(s):  
Integral Equation ◽  
Fixed Point ◽  
Fixed Point Theorem ◽  
Global Convergence ◽  
Point Theorem ◽  
Newton’S Method ◽  
Newton's Method ◽  
Linear Integral Equation ◽  
The Fixed Point Theorem ◽  
Linear Integral

We obtain results of restricted global convergence for Newton’s method from ideas based on the Fixed-Point theorem and using the Newtonian operator and auxiliary points. The results are illustrated with a non-linear integral equation of Davis-type and improve the results previously given by the authors.

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