• East Asian mathematical journal
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• v.23 no.2
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• pp.229-246
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• 2007

Some inequalities related to the $H{\ddot{o}}lder$ integral inequality and applications for bounding the ${\check{C}}eby{\check{s}}ev$ functional are given.

• Communications of the Korean Mathematical Society
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• v.30 no.2
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• pp.81-92
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• 2015

In this paper, we aim at establishing a generalized fractional integral version of Gr$\ddot{u}$ss type integral inequality by making use of the Gauss hypergeometric function fractional integral operator. Our main result, being of a very general character, is illustrated to specialize to yield numerous interesting fractional integral inequalities including some known results.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.5
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• pp.806-811
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• 2017

This paper considers the delay-dependent stability of linear systems with a time-varying delay in the frame work of Lyapunov-Krasovskii functional(LKF) approach. In this approach, an integral inequality is essential to estimate the upper bound of time-derivative of LKF, and a less conservative one is needed to get a less conservative stability result. In this paper, based on free weighting matrices, an improved integral inequality encompassing well-known results is proposed and then a stability result in the form of linear matrix inequality is derived based on an augmented LKF. Finally, two well-known numerical examples are given to demonstrate the usefulness of the proposed result.

• Bulletin of the Korean Mathematical Society
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• v.46 no.1
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• pp.125-134
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• 2009

In the present paper, we give several discrete results for the open problem posed in the article [Feng Qi, Several integral inequalities, J. Inequal. Pure and Appl. Math. 1(2000), no. 2, Art. 19].

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.377-388
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• 2002

In this paper, we obtain an extension of an analogue of Hilbert's inequality involving series of nonnegative terms. The integral analogies of the main results are also given.

• Kyungpook Mathematical Journal
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• v.52 no.4
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• pp.397-404
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• 2012

In this article, the reverse q-H$\ddot{o}$lder type inequality and two dimensional q-H$\ddot{o}$lder's inequality are established. We also obtain some q-integral inequalities by using q-H$\ddot{o}$lder's inequality which give q-Hardy's inequalities as spacial cases.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.131-152
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• 2010

In this paper, by introducing some parameters we establish an extension of Hardy-Hilbert's integral inequality and the corresponding inequality for series. As an application, the reverses, some particular results and their equivalent forms are considered.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.1
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• pp.161-166
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• 2018

This paper deals an impulsive fractional integral inequality with singular kernel which can be used in getting the explicit estimate of solutions of impulsive fractional differential equations.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.5 no.2
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• pp.117-136
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• 2001

A generalization of Ostrowski integral inequality for mappings whose derivatives are bounded and applications for general quadrature formulae are given.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.227-237
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• 2021

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.