A class of nonlinear delay integral inequalities for two-variable functions and their applications in Volterra integral equations

Volume 32, Issue 1, pp 1--12 http://dx.doi.org/10.22436/jmcs.032.01.01

Publication Date: June 01, 2023 Submission Date: March 24, 2023 Revision Date: May 06, 2023 Accteptance Date: May 10, 2023

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Authors

S. Kriket - Department of Mathematics and Computer Science, University of Ghardaia, Ghardaia, Algeria. A. Boudeliou - Department of Mathematics, University of Constantine 1, BP 325, Ain El Bey Street, Constantine 25017, Algeria.

Abstract

In this paper, we establish some new nonlinear integral inequalities with delay in two independent variables which generalize some known inequalities recently obtained. These results can be used as handy tools to study the boundedness of solutions of Volterra integral equations. An application is given to illustrate how our results can be applied to study the boundedness of the solutions of certain Volterra equations.

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Keywords

• Delay integral inequality
• two-variable functions
• properties of solutions
• Volterra integral equation

MSC

•  26D10
•  26D15
•  45D05
•  45G10

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