• Kyungpook Mathematical Journal
• /
• v.27 no.2
• /
• pp.153-161
• /
• 1987

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

• Kyungpook Mathematical Journal
• /
• v.54 no.4
• /
• pp.555-575
• /
• 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.

• Kyungpook Mathematical Journal
• /
• v.27 no.2
• /
• pp.145-152
• /
• 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.

• Honam Mathematical Journal
• /
• v.45 no.1
• /
• pp.54-70
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.43 no.3
• /
• pp.563-578
• /
• 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.

• Journal of the Chungcheong Mathematical Society
• /
• v.26 no.1
• /
• pp.71-84
• /
• 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
• /
• v.18 no.1
• /
• pp.63-78
• /
• 2011

In the present paper, we obtain integral inequalities involving the Kurzweil-Stieltjes integrals which generalize Gronwall-Bellman inequality and we use the inequalities to verify existence of solutions of a certain integral equation. Such inequalities will play an important role in the study of impulsively perturbed systems [9].

• Kyungpook Mathematical Journal
• /
• v.60 no.1
• /
• pp.211-222
• /
• 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.

• Journal of applied mathematics & informatics
• /
• v.26 no.5_6
• /
• pp.877-888
• /
• 2008

This paper deals with some new nonlinear delay and weakly singular integral inequalities of Gronwall-Bellman type. These results generalize the inequalities discussed by Xiang and Kuang [19]. Several other inequalities proved by $Medve{\check{d}}$ [15] and Ou-Iang [17] follow as special cases of this paper. This work can be used in the analysis of various problems in the theory of certain classes of differential equations, integral equations and evolution equations. A modification of the Ou-Iang type inequality with delay is also treated in this paper.