Generalization of some retarded integral inequalities with power in two independent variables and applications

Selma Mili; Ammar Boudeliou; Selma Mili; Ammar Boudeliou

doi:10.3934/math.2025191

AIMS Mathematics

2025, Volume 10, Issue 2: 4120-4138. doi: 10.3934/math.2025191

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Generalization of some retarded integral inequalities with power in two independent variables and applications

Selma Mili ,
Ammar Boudeliou ^,

Department of Mathematics, University of Constantine 1 Brothers Mentouri, BP, 325, Ain El Bey Street, 25017, Algeria

Received: 05 November 2024 Revised: 18 January 2025 Accepted: 20 February 2025 Published: 27 February 2025
MSC : 26D10, 26D15, 45D05

In this work, some new kinds of nonlinear power integral inequalities in two-dimensional cases are introduced. With advanced analytical mathematical methods, many estimations are obtained in order to generalize to higher order, well known results in the literature for $ p = 1 $ and $ p\in(0, 1] $. As an example, we apply these results to determine the boundedness of solutions of nonlinear bidimensional Volterra type integral equations for $ p > 1 $.
- boundedness,
- retarded integral inequality,
- power,
- Volterra integral equation
Citation: Selma Mili, Ammar Boudeliou. Generalization of some retarded integral inequalities with power in two independent variables and applications[J]. AIMS Mathematics, 2025, 10(2): 4120-4138. doi: 10.3934/math.2025191

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Abstract

In this work, some new kinds of nonlinear power integral inequalities in two-dimensional cases are introduced. With advanced analytical mathematical methods, many estimations are obtained in order to generalize to higher order, well known results in the literature for $ p = 1 $ and $ p\in(0, 1] $. As an example, we apply these results to determine the boundedness of solutions of nonlinear bidimensional Volterra type integral equations for $ p > 1 $.

References

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