Existence and uniqueness of the solution for a general system of Fredholm integral equations

Filip, Alexandru-Darius; Petruşel, Adrian

doi:10.1002/mma.6737

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…Proof. It can be found in reference [27]. e solution (u 1 , u 2 ) ∈ (L 2 [0, 1]) 2 of the system is sought in equation ( 2) which can be rewritten in the following form:…”

Section: Existence and Uniquenessmentioning

confidence: 99%

A Combination of Bernstein and Improved Block-Pulse Functions for Solving a System of Linear Fredholm Integral Equations

Taha

Ramadan

et al. 2022

Mathematical Problems in Engineering

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The present paper illustrates a new numerical technique to solve a system of linear Fredholm integral equations of the second kind. The current work introduces a coupling between hybrid Bernstein functions and improved block-pulse functions (HBI). The current method transforms the linear second kind Fredholm integral equations system into an algebraic system that can be solved by using classical methods. Some numerical examples are introduced to validate the new approach. The results showed that the method is promising, powerful, ultimately accurate, and highly efficient.

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“…Proof. It can be found in reference [27]. e solution (u 1 , u 2 ) ∈ (L 2 [0, 1]) 2 of the system is sought in equation ( 2) which can be rewritten in the following form:…”

Section: Existence and Uniquenessmentioning

confidence: 99%

A Combination of Bernstein and Improved Block-Pulse Functions for Solving a System of Linear Fredholm Integral Equations

Taha

Ramadan

et al. 2022

Mathematical Problems in Engineering

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“…Hence, we obtain the so called Rus' variant of Maia's fixed point theorem. More considerations can be found in [5][6][7][8]12] and [2].…”

Section: Maia's Fixed Point Theoremmentioning

confidence: 99%

Some applications of Maia's fixed point theorem in the case of operators with Volterra property with respect to a subinterval

Filip¹

2022

MMN

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The aim of this paper is to improve some fixed point results given by I. A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes ¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia's theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes ¸-Bolyai Univ. Cluj-Napoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia's fixed point theorem.

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“…Hence, we obtain the so called Rus' variant of Maia's fixed point theorem. More considerations can be found in [8], [6], [7], [12], [5] and [2].…”

Section: Maia's Fixed Point Theoremmentioning

confidence: 99%

Some applications of Maia's fixed point theorem in the case of operators with Volterra property with respect to a subinterval

Filip¹

2022

MMN

View full text Add to dashboard Cite

The aim of this paper is to improve some fixed point results given by I.A. Rus in (On a fixed point theorem of Maia, Studia Univ. Babes¸-Bolyai Math., 22(1977), 40-42), (Basic problem for Maia’s theorem, Sem. on Fixed Point Theory, Preprint 3(1981), Babes¸-Bolyai Univ. ClujNapoca, 112-115) and (Data dependence of the fixed points in a set with two metrics, Fixed Point Theory, 8(2007), no. 1, 115-123), by applying, instead of contraction principle, some variants of Maia’s fixed point theorem.

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Existence and uniqueness of the solution for a general system of Fredholm integral equations

Abstract: The aim of this paper is to present existence and uniqueness results for the solution of a general system of Fredholm integral equations by applying the vectorial form of Maia's fixed‐point theorem. A Gronwall‐type lemma and comparison theorems are also obtained.

Cited by 4 publications

References 7 publications

A Combination of Bernstein and Improved Block-Pulse Functions for Solving a System of Linear Fredholm Integral Equations

A Combination of Bernstein and Improved Block-Pulse Functions for Solving a System of Linear Fredholm Integral Equations

Some applications of Maia's fixed point theorem in the case of operators with Volterra property with respect to a subinterval

Some applications of Maia's fixed point theorem in the case of operators with Volterra property with respect to a subinterval

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