On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations

By some new analysis techniques, we generalize the results presented by Pachpatte in [Integral and Finite Difference Inequalities and Applications, volume 205, Elsevier, 2006] and and by S. D. Kendre in [Some nonlinear integral inequalities for Volterra–Fredholm integral equations, Adv. Inequal. App...

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Main Authors:	A.A. El-Deeb, Reda Gamal Ahmed
Format:	Article
Language:	English
Published:	SpringerOpen 2017-07-01
Series:	Journal of the Egyptian Mathematical Society
Subjects:	Gronwall–Bellman inequality Retarded integral and differential equations Volterra–Fredholm integral equation
Online Access:	http://www.sciencedirect.com/science/article/pii/S1110256X17300093

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spelling	doaj-85c9b9b5a46a4e7992ce0045db26ac162020-11-24T21:50:06ZengSpringerOpenJournal of the Egyptian Mathematical Society1110-256X2017-07-0125327928510.1016/j.joems.2017.02.001On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equationsA.A. El-DeebReda Gamal AhmedBy some new analysis techniques, we generalize the results presented by Pachpatte in [Integral and Finite Difference Inequalities and Applications, volume 205, Elsevier, 2006] and and by S. D. Kendre in [Some nonlinear integral inequalities for Volterra–Fredholm integral equations, Adv. Inequal. App, 2014:Article 21, 2014.] to nonlinear retarded inequalities, and investigate also some new forms. Some applications are also presented in order to illustrate the usefulness of some of our results.http://www.sciencedirect.com/science/article/pii/S1110256X17300093Gronwall–Bellman inequalityRetarded integral and differential equationsVolterra–Fredholm integral equation
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	A.A. El-Deeb Reda Gamal Ahmed
spellingShingle	A.A. El-Deeb Reda Gamal Ahmed On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations Journal of the Egyptian Mathematical Society Gronwall–Bellman inequality Retarded integral and differential equations Volterra–Fredholm integral equation
author_facet	A.A. El-Deeb Reda Gamal Ahmed
author_sort	A.A. El-Deeb
title	On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations
title_short	On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations
title_full	On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations
title_fullStr	On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations
title_full_unstemmed	On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations
title_sort	on some generalizations of certain nonlinear retarded integral inequalities for volterra–fredholm integral equations and their applications in delay differential equations
publisher	SpringerOpen
series	Journal of the Egyptian Mathematical Society
issn	1110-256X
publishDate	2017-07-01
description	By some new analysis techniques, we generalize the results presented by Pachpatte in [Integral and Finite Difference Inequalities and Applications, volume 205, Elsevier, 2006] and and by S. D. Kendre in [Some nonlinear integral inequalities for Volterra–Fredholm integral equations, Adv. Inequal. App, 2014:Article 21, 2014.] to nonlinear retarded inequalities, and investigate also some new forms. Some applications are also presented in order to illustrate the usefulness of some of our results.
topic	Gronwall–Bellman inequality Retarded integral and differential equations Volterra–Fredholm integral equation
url	http://www.sciencedirect.com/science/article/pii/S1110256X17300093
work_keys_str_mv	AT aaeldeeb onsomegeneralizationsofcertainnonlinearretardedintegralinequalitiesforvolterrafredholmintegralequationsandtheirapplicationsindelaydifferentialequations AT redagamalahmed onsomegeneralizationsofcertainnonlinearretardedintegralinequalitiesforvolterrafredholmintegralequationsandtheirapplicationsindelaydifferentialequations
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On some generalizations of certain nonlinear retarded integral inequalities for Volterra–Fredholm integral equations and their applications in delay differential equations

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