• 대한수학회보
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• 제42권4호
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• pp.789-805
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• 2005

In this paper we consider analogous of Gronwall-type inequalities involving iterated integrals in the inequality (1.2) for functions when the function u in the right-hand side of the in­equality (1.2) is replaced by the function $u^P$ for some p. These inequalities are effective tools in the study of a system of an integral equation. We also provide some integral inequalities involving iterated integrals.

• Kyungpook Mathematical Journal
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• 제27권2호
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• pp.153-161
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• 1987

In this paper we present several nonlinear generalization of Gronwall-Bellman-Reid inequalities. These results provided genuine upper estimates.

• Kyungpook Mathematical Journal
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• 제54권4호
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• pp.555-575
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• 2014

In this paper, we establish some new nonlinear integral inequalities of Gronwall-Bellman type. These inequalities generalize some famous inequalities which can be used in applications as handy tools to study the qualitative as well as quantitative properties of solutions of some nonlinear ordinary differential and integral equations. More accurately we extend certain results which have been proved in A. Abdeldaim and M. Yakout [1] and H. El-Owaidy, A. A. Ragab, A. Abdeldaim [7] too.

• East Asian mathematical journal
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• 제34권3호
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• pp.249-263
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• 2018

We aim to establish certain Gronwall type inequalities associated with Riemann-Liouville k- and Hadamard k-fractional derivatives. The results presented here are sure to be new and potentially useful, in particular, in analyzing dependence solutions of certain k-fractional differential equations of arbitrary real order with initial conditions. Some interesting special cases of our main results are also considered.

• 호남수학학술지
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• 제45권1호
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• pp.54-70
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• 2023

In this article, we state and prove several new retarded nonlinear integral and integro-differential inequalities of Gronwall-Bellman-Pachpatte type. These inequalities generalize some former famous inequalities and can be used in examining the existence, uniqueness, boundedness, stability, asymptotic behaviour, quantitative and qualitative properties of solutions of nonlinear differential and integral equations. Applications are provided to demonstrate the strength of our inequalities in estimating the boundedness and global existence of the solution to initial value problem for nonlinear integro-differential equation and Volterra type retarded nonlinear equation. This research work will ensure to open the new opportunities for studying of nonlinear dynamic inequalities on time scale structure of varying nature.

• 대한수학회지
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• 제45권2호
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• pp.331-353
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• 2008

Some new nonlinear retarded integral inequalities of Gronwall-like type are established, which mainly generalized some results given by Cho, Dragomir and Kim (J. Korean Math. Soc. 43 (2006), No.3, pp. 563-578) and can be used in the analysis of various problems in the theory of certain classes of differential equations and integral equations. Applications examples are also indicated.

• 대한수학회지
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• 제43권3호
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• pp.563-578
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• 2006

The main aim of the present paper is to establish some new Gronwall type inequalities involving iterated integrals and give some applications of the main results.

• Kyungpook Mathematical Journal
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• 제27권2호
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• pp.145-152
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• 1987

In this paper we wish to establish some new integral in equalities of the Gronwall-Bellman-Reid type that have a wide range of applications in the differential and integral equations.

• 충청수학회지
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• 제20권4호
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• pp.561-568
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• 2007

In this paper, we improve the results of [9] and give an application to boundedness of the solutions of nonlinear integro-differential equations.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.211-222
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• 2020

Integral inequalities provide a very useful and handy tool for the study of qualitative as well as quantitative properties of solutions of differential and integral equations. The main object of this work is to generalize some integral inequalities of quadratic type not only for integer order but also for arbitrary (fractional) order. We also study some inequalities of Pachpatte type.