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Dalila Bitat
Hassane Khellaf

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Dalila Bitat
Hassane Khellaf

WSEAS Transactions on Mathematics

Print ISSN: 1109-2769
E-ISSN: 2224-2880

Volume 17, 2018

Notice: As of 2014 and for the forthcoming years, the publication frequency/periodicity of WSEAS Journals is adapted to the 'continuously updated' model. What this means is that instead of being separated into issues, new papers will be added on a continuous basis, allowing a more regular flow and shorter publication times. The papers will appear in reverse order, therefore the most recent one will be on top.

Volume 17, 2018

On Some Non-Linear Integral Inequalities for Two-Variable Functions with Delay Involving Integration over Infinite Intervals

AUTHORS: Dalila Bitat, Hassane Khellaf

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ABSTRACT: In this paper, we present some non-linear integral inequalities with a term of delay for functions of two independent variables that can be used in the theory of differential and integral equations with time delay. Also, we generalize these inequalities by integration over infinite intervals. An application is given as an illustration

KEYWORDS: Non-linear integral inequalities with delay; Two independent variables; Non-decreasing functions; Differential and integral equations with delay; Integration over infinite intervals


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[2] Ghrissi, T., and M. A. Hammami. Generalized retarded integral inequalities of Gronwall type and applications. WSEAS Transactions on Mathematics. Vol. 16, 2017, pp. 173-182.

[3] Jiang, F. C., and F. W. Meng. Explicit bounds on some new non-linear integral inequality with delay. Journal of Computational and Applied Mathematics. No. 205, 2007, pp. 479-487.

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[5] Mi, Y. Some generalized Gronwall-Bellman type impulsive integral inequalities and their applications. Journal of Applied Mathematics. 2014.

[6] Pachpatte, B.G. On a certain retarded integral inequality and its applications. Journal of Inequalities in Pure and Applied Mathematics. Vol. 5, No. 1, 2004.

[7] Qingling, G., and Q. Zhonghua. A generalized retarded Gronwall-like inequalities. Applied Mathematical Sciences. Vol. 7, No. 99, 2013, pp. 4943-4948.

[8] Xu, R., and X. Ma. Some new retarded nonlinear Volterra-Fredholm type integral inequalities with maxima in two variables and their applications. Journal of Inequalities and Applications. No. 187, 2017.

[9] Zhang, H., and F. Meng. Integral inequalities in two independent variables for retarded Volterra equations. Applied Mathematics and Computation. No. 199, 2008, pp. 90-98.

WSEAS Transactions on Mathematics, ISSN / E-ISSN: 1109-2769 / 2224-2880, Volume 17, 2018, Art. #19, pp. 137-154

Copyright © 2018 Author(s) retain the copyright of this article. This article is published under the terms of the Creative Commons Attribution License 4.0

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