An extension of Darbo’s theorem and its application to existence of solution for a system of integral equations

Banaei, Shahram

doi:10.1080/25742558.2019.1614319

Cited by 8 publications

(4 citation statements)

References 10 publications

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“…Heretofore, applying MNC approaches many articles have been extracted on the existence and behavior of solutions for nonlinear differential and integral equations. Some of these papers are [2,3,6,7,11,14].…”

Section: Introductionmentioning

confidence: 99%

Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

Banaei¹,

Parvaneh²,

Mursaleen³

2021

CJM

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"In this article, applying the concept of measure of noncompactness, some fixed point theorems in the Fréchet space $L^\infty(\mathfrak{G})$ (where $\mathfrak{G}\subseteq \mathbb{R}^{\omega}$) have been proved. We handle our obtained consequences to inquiry the existence of solutions for infinite systems of Urysohn type integral equations. Our results extend some famous related results in the literature. Finally, to indicate the effectiveness of our results we present a genuine example."

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Section: Introductionmentioning

confidence: 99%

Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

Banaei¹,

Parvaneh²,

Mursaleen³

2021

CJM

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“…For more details on the theory of measure of noncompactness, its applications and its relations with nonlinear analysis we refer the reader to [8][9][10][11][12][13].…”

Section: Introductionmentioning

confidence: 99%

Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

et al. 2020

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“…This notion is also applied in studies of the existence of solutions of ODE and PDE problems, integral and integro-differential equations, etc. For more details, we refer the reader to [2][3][4][5][6]. In [7], the authors generalized the Darbo's fixed point theorem via the concept of the class of operators O( f ; .…”

Section: Introductionmentioning

confidence: 99%

On New Extensions of Darbo’s Fixed Point Theorem with Applications

et al. 2020

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In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

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An extension of Darbo’s theorem and its application to existence of solution for a system of integral equations

Cited by 8 publications

References 10 publications

Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

Measures of noncompactness and infinite systems of integral equations of Urysohn type in $L^\infty(\mathfrak{G})$

Existence of Solutions for a System of Integral Equations Using a Generalization of Darbo’s Fixed Point Theorem

On New Extensions of Darbo’s Fixed Point Theorem with Applications

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