A numerical method for solvability of some non-linear functional integral equations

Deep, Amar; Deepmala, _; Rabbani, Mohsen

doi:10.1016/j.amc.2020.125637

Cited by 19 publications

(5 citation statements)

References 22 publications

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“…By unifying and enlarging the earlier results of [12,15,29,34] and using Petryshyn's fixed point, we obtained a new method to prove the existence of solutions for some functional integral equations. The merit of Theorem 3.1 among the others (Darbo's and Schauder fixed point theorem) lies in that in applying this theorem, here one does not need to confirm the involved operator maps is on a closed convex subset onto itself.…”

Section: Discussionmentioning

confidence: 98%

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Solvability for two dimensional functional integral equations via Petryshyn’s fixed point theorem

Deep

Dhiman

Hazarika

et al. 2021

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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This paper aims to use the Petryshyn's fixed point theorem associated with the measure of non-compactness to prove the existence of solutions of two-dimensional functional integral equations in the Banach algebra of continuous functions on the interval C([0, a] × [0, â], R), a, â > 0. Our existence results contains many functional integral equations as special case that arise in nonlinear analysis. Finally, we present some examples which show that our result is useful for various class of equations.

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Section: Discussionmentioning

confidence: 98%

“…Several authors examined an equation similar to (1) and their basic and good idea was the construction of an MNC with Darbo's fixed point theorem in the Banach algebra C[0, a] (see [4,5,15,29,34]). In our study, we apply Petryshyn's theorem (prefer over Darbo's theorem) to examine the solvability of Eq.…”

Section: Introductionmentioning

confidence: 99%

Solvability for two dimensional functional integral equations via Petryshyn’s fixed point theorem

Deep

Dhiman

Hazarika

et al. 2021

Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat.

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“…Furthermore, several attractive outcomes concerning applications of fixed point methods, various fixed point theorems, and EUSs, several other qualitative properties with regard to certain IEs and IDEs can be found in the books of Abbas et al [18] and Burton [19], and the papers of Chauhan et al [20], Deep et al [21], Graef et al [22], Lungu and Rus [23], Khan et al [24,25], Tunç and Tunç [26,27], Tunç et al [27,28], and their references.…”

Section: ) and The Kernelmentioning

confidence: 99%

Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations

Tunç,

Alshammari,

Akyildiz

2023

Symmetry

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The authors deal with nonlinear and general Hammerstein-type functional integral equations (HTFIEs). The first objective of this work is to apply and extend Burton’s method to general and nonlinear HTFIEs in a Banach space via the Chebyshev norm and complete metric. The second objective of the paper is to extend and improve some earlier results to nonlinear HTFIEs. The authors prove two new theorems with regard to the existence and uniqueness of solutions (EUSs) of HTFIEs via a technique called progressive contractions, which belongs to T. A. Burton, and the Chebyshev norm and complete metric.

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“…Furthermore, several interesting results in the sense of Ulam stabilities, Lyapunov stabilities, some other related results with regard to qualitative behaviors of solutions for disparate classes of the IDEs, IEs and so on have been discussed by Chauhan et al [23], Deep et al [24], Gãvruţa [25], Graef and Tunç [26], Hammami and Hnia [27], Ngoc et al [17], Petruşel et al [28], Radu [29], Rassias [30], Shah et al [31], ) and in the books or the articles cited in these sources together that are presented in the above ones.…”

Section: Introductionmentioning

confidence: 99%

On Ulam Stabilities of Delay Hammerstein Integral Equation

Tunç,

Tunç

2023

Symmetry

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In this paper, we consider a Hammerstein integral equation (Hammerstein IE) in two variables with two variables of time delays. The aim of this paper is to investigate the Hyers–Ulam (HU) stability and Hyers–Ulam–Rassias (HUR) stability of the considered IE via Banach’s fixed point theorem (Banach’s FPT) and the Bielecki metric. The proofs of the new outcomes of this paper are based on these two basic tools. As the new contributions of the present study, here, for the first time, we develop the outcomes that can be found in the earlier literature on the Hammerstein IE, including variable time delays. The present study also includes complementary outcomes for the symmetry of Hammerstein IEs. Finally, a concrete example is given at the end of this study for illustrations.

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A numerical method for solvability of some non-linear functional integral equations

Cited by 19 publications

References 22 publications

Solvability for two dimensional functional integral equations via Petryshyn’s fixed point theorem

Solvability for two dimensional functional integral equations via Petryshyn’s fixed point theorem

Existence and Uniqueness of Solutions of Hammerstein-Type Functional Integral Equations

On Ulam Stabilities of Delay Hammerstein Integral Equation

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