Domains of global convergence for a type of nonlinear Fredholm-Nemytskii integral equations

Ezquerro, J. A.; Hernández‐Verón, M. A.

doi:10.1016/j.apnum.2019.08.004

Cited by 6 publications

(3 citation statements)

References 10 publications

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“…In Sect. 3, we do this study from the application of the restricted Fixed Point Theorem given above to the operator W and using a technique based on auxiliary points [10][11][12]. Moreover, we approximate a fixed point φ * of the operator (4) by the iterative method (3) starting at any function of the considered domain.…”

Section: Mjommentioning

confidence: 99%

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Location of Solutions of Fredholm–Nemytskii Integral Equations from a Whittaker-Type Operator

Ezquerro

Hernández‐Verón

2022

Mediterr. J. Math.

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We analyse the global convergence of a Whittaker-type iterative method and obtain restricted global convergence domains, so that we can locate and separate solutions of Fredholm–Nemytskii nonlinear integral equations by means of balls. For this, we use two techniques, one based on the well-known fixed point theorem and the other on a system of recurrence relations. In both techniques, we use the Whittaker-type operator involved and auxiliary functions.

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Section: Mjommentioning

confidence: 99%

“…Next, we present a new result of uniqueness of the fixed point under the conditions (11) or (12), where a technique of functional analysis is used.…”

Section: )mentioning

confidence: 99%

Location of Solutions of Fredholm–Nemytskii Integral Equations from a Whittaker-Type Operator

Ezquerro

Hernández‐Verón

2022

Mediterr. J. Math.

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“…In [1], we use a technique based on the use of auxiliary points [2,3] to present a study of the convergence of Newton's method in which we obtain global convergence balls of the form B( x, R), where x is an auxiliary point. These balls allow us to locate a solution of the equation F(x) = 0 and separate it from other possible solutions.…”

Section: Introductionmentioning

confidence: 99%