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Research Article | Open Access

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
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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 ∈ ( 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.

Keywords

boundednessretarded integral inequalitypowerVolterra integral equation
CLC number: 26D10, 26D15, 45D05

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 4120-4138
DOI: 10.3934/math.2025191

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Cite this article:
Mili S, Boudeliou A. Generalization of some retarded integral inequalities with power in two independent variables and applications. AIMS Mathematics, 2025, 10(2): 4120-4138. https://doi.org/10.3934/math.2025191

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Received: 05 November 2024
Revised: 18 January 2025
Accepted: 20 February 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)