Solvability of functional quadratic integral equations with perturbation

Metwali, Mohamed M. A.

doi:10.7494/opmath.2013.33.4.725

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Cited by 4 publications

(2 citation statements)

References 30 publications

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“…Obviously ζ is neither continuous nor bounded. To get the existence of solutions to Equation (8), which is a particular case of (1), we set…”

Section: Examplesmentioning

confidence: 99%

FUNCTIONAL QUADRATIC INTEGRAL EQUATIONS IN L 1 loc(R +) LATIFA BENHAMOUCHE AND SMA¨IL DJEBALI

2019

Electronic Journal of Mathematical Analysis and Applications

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In this work, we study the existence of solutions for a class of functional quadratic integral equations of Volterra type in the space L 1 loc (R + ). The main result of this paper is obtained by applying the Schauder-Tychonov fixed point theorem combined with Ascoli-Arzéla Lemma and Dunford-Pettis compactness criterion. It generalizes some previous results obtained in [12] and [13]. Two illustrative examples are included.

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“…Obviously ζ is neither continuous nor bounded. To get the existence of solutions to Equation (8), which is a particular case of (1), we set…”

Section: Examplesmentioning

confidence: 99%

FUNCTIONAL QUADRATIC INTEGRAL EQUATIONS IN L 1 loc(R +) LATIFA BENHAMOUCHE AND SMA¨IL DJEBALI

2019

Electronic Journal of Mathematical Analysis and Applications

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“…In [27] the author used the measure of weak noncompactness with Krasnoselskii fixed point theory to find L 1 (R + ) -solutions of the equation…”

Section: Introductionmentioning

confidence: 99%

Solvability of Gripenberg's equations of fractional order with perturbation term in weighted LpL_p-spaces on R+{\mathbb{R}}^+

2021

Turk J Math

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This article deals with the solvability of Gripenberg's equations of fractional order with a perturbation term in weighted Lebesgue spaces on R + = [0, ∞) via the fixed point hypothesis and the measure of noncompactness. The uniqueness of the solutions for the studied problem is discussed. An example is included to validate our results. The results presented in the article extend and generalize some former results in the available literature.

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On a Class of Quadratic Urysohn–Hammerstein Integral Equations of Mixed Type and Initial Value Problem of Fractional Order

Metwali

2015

Mediterr. J. Math.

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Solvability of functional quadratic integral equations with perturbation

Abstract: Abstract. We study the existence of solutions of the functional quadratic integral equation with a perturbation term in the space of Lebesgue integrable functions on an unbounded interval by using the Krasnoselskii fixed point theory and the measure of weak noncompactness.

Cited by 4 publications

References 30 publications

FUNCTIONAL QUADRATIC INTEGRAL EQUATIONS IN L 1 loc(R +) LATIFA BENHAMOUCHE AND SMA¨IL DJEBALI

FUNCTIONAL QUADRATIC INTEGRAL EQUATIONS IN L 1 loc(R +) LATIFA BENHAMOUCHE AND SMA¨IL DJEBALI

Solvability of Gripenberg's equations of fractional order with perturbation term in weighted LpL_p-spaces on R+{\mathbb{R}}^+

On a Class of Quadratic Urysohn–Hammerstein Integral Equations of Mixed Type and Initial Value Problem of Fractional Order

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