• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.71-84
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• 2013

In this paper we study some nonlinear Pachpatte type integral inequalities on time scales by using a Bihari type inequality. Our results unify some continuous inequalities and their corresponding discrete analogues, and extend these inequalities to dynamic inequalities on time scales. Furthermore, we give some examples concerning our results.

• The Pure and Applied Mathematics
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• v.21 no.1
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• pp.61-75
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• 2014

The purpose of this paper is to obtain some integral inequalities with impulses by using the method of Stieltjes derivatives, and we use our results in the study of Lyapunov stability of solutions of a certain nonlinear impulsive integro-differential equation.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.559-571
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• 2004

The aim of the present paper is to establish some nonlinear integral inequalities in two independent variables which provide explicit bounds on unknown functions. The inequalities given here can be used as tools in the qualitative theory of certain partial differential equations.

• The Pure and Applied Mathematics
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• v.23 no.2
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• pp.181-199
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• 2016

In this paper we obtain some retarded integral inequalities involving Stieltjes derivatives and we use our results in the study of various qualitative properties of a certain retarded impulsive differential equation.

• Kyungpook Mathematical Journal
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• v.54 no.4
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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.

• Bulletin of the Korean Mathematical Society
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• v.41 no.4
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• pp.633-639
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• 2004

In this paper using integral representations for n-time differentiable mappings, we establish new generalizations of certain Ostrowski and Trapezoid type inequalities by using fairly elementary analysis.

• Kyungpook Mathematical Journal
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• v.49 no.4
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• pp.623-630
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• 2009

This paper deals with some new generalizations of the Hardy-Hilbert type integral inequalities with some parameters. We also consider the equivalent inequalities and the reverse forms.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.47-56
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• 2024

It is well known that inequalities enable us to analyze and solve complex problems with precision and efficiency. The inequalities provide powerful tools for establishing bounds, optimizing solutions, and deepening our understanding of mathematical concepts, paving the way for advancements in areas such as optimization, analysis, and probability theory. In this paper, we present some properties for Hadamard-Simpsons type inequalities in the classic integral and Riemann-Liouville fractional integral. We use the convexity of the given function and its first derivative.

• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.107-114
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• 2018

We establish some new ostrowski type inequalities for MT-convex function including first order derivative via Niemann-Trouvaille fractional integral. It is interesting to mention that our results provide new estimates on these types of integral inequalities for MT-convex functions.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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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.