• The Transactions of The Korean Institute of Electrical Engineers
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• v.65 no.3
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• pp.457-462
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• 2016

In this paper, we consider the stability of time-delayed linear systems. To derive an LMI form of result, the integral inequality is essential, and Jensen's integral inequality was the best in the last two decades until Seuret's integral inequality is appeared recently. However, these two are proportional to the inverse of integration interval, so another integral inequality is needed to make it in the form of LMI. In this paper, we derive an integral inequality which is proportional to the integration interval which can be easily converted into LMI form without any other inequality. Also, it is shown that Seuret's integral inequality is a special case of our result. Next, based on this new integral inequality, we derive a stability condition in the form of LMI. Finally, we show, by well-known two examples, that our result is less conservative than the recent results.

• Bulletin of the Korean Mathematical Society
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• v.56 no.6
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• pp.1423-1433
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• 2019

Here we present the right and left Riemann-Liouville fractional fundamental theorems of fractional calculus without any initial conditions for the first time. Then we establish a Riemann-Liouville fractional Polya type integral inequality with the help of generalised right and left Riemann-Liouville fractional derivatives. The amazing fact here is that we do not need any boundary conditions as the classical Polya integral inequality requires. We extend our Polya inequality to Choquet integral setting.

• Kyungpook Mathematical Journal
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• v.49 no.3
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• pp.563-572
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• 2009

In this paper, by introducing some parameters and using the way of weight function, a new integral inequality with a best constant factor is given, which is a relation between Hilbert's integral inequality and a Hilbert-type inequality. As applications, the equivalent form, the reverse forms and some particular inequalities are considered.

• Korean Journal of Mathematics
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• v.29 no.3
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• pp.467-472
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• 2021

In this paper, we give some new Copson-type integral inequality with a sharp constant.

• Kyungpook Mathematical Journal
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• v.50 no.2
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• pp.297-306
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• 2010

In this paper, the integral operator is used. We give a new Hilbert-type integral inequality, whose kernel is the homogeneous form with degree - $\lambda$ and with three pairs of conjugate exponents and the best constant factor and its reverse form are also derived. It is shown that the results of this paper represent an extension as well as some improvements of the earlier results.

• Honam Mathematical Journal
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• v.43 no.3
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• pp.441-452
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• 2021

In this paper, improved power-mean integral inequality, which provides a better approach than power-mean integral inequality, is proved. Using Hölder-İşcan integral inequality and improved power-mean integral inequality, some inequalities of Hadamard's type for functions whose derivatives in absolute value at certain power are quasi-convex are given. In addition, the results obtained are compared with the previous ones. Then, it is shown that the results obtained together with identity are better than those previously obtained.

• East Asian mathematical journal
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• v.22 no.1
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• pp.17-35
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• 2006

Some additive reverses of the continuous triangle inequality for Bochner integral of vector-valued functions in Banach spaces are given. Applications for complex-valued functions are considered as well.

• Kyungpook Mathematical Journal
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• v.52 no.3
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• pp.291-298
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• 2012

In this paper, by estimating the weight function, we give a new Hilbert-type inequality with the integral in whole plane. As its applications, we consider the equivalent and a particular result.

• Kyungpook Mathematical Journal
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• v.49 no.2
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• pp.393-401
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• 2009

By introducing a parameter and estimating the weight coefficient, we obtain a new Hilbert-type integral inequality with a composite kernel and a best constant factor. As applications, we also consider its equivalent forms and reverse forms.

• Kyungpook Mathematical Journal
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• v.48 no.1
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• pp.93-100
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• 2008

In this paper, by introducing some parameters and estimating the weight function, we give a new Hilbert-type integral inequality with a best constant factor. The equivalent inequality and the reverse forms are considered.