• The Pure and Applied Mathematics
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• v.15 no.1
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• pp.93-101
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• 2008

In this article we shall characterize the Heinz-Kato-Furuta inequality in several ways, and the best bound for sharpening of the inequality is obtained by the method in [7].

• Honam Mathematical Journal
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• v.41 no.1
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• pp.89-99
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• 2019

The Steffensen's Inequality was discovered in 1918 by Johan Frederic Steffensen (1873-1961). This inequality is very popular in the research environment and attracted the attention of many people working in similar area. Various extensions and generalisations have been provided concerning the inequality. This paper presents some further refinements of the Steffensen's Inequality on Time scales using methods of convexity, differentiability and monotonicity.

• 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.

• Journal of the Chungcheong Mathematical Society
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• v.31 no.2
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• pp.231-237
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• 2018

Hardy's inequality is refined non-trivially as the form $${\int_{0}^{{\infty}}}\{{\frac{1}{x}}{\int_{0}^{x}}f(t)dt\}^pdx{\leq}Q_f{\times}({\frac{p}{p-1}})^p{\int_{0}^{x}}f^p(x)dx$$ for some $Q_f:0{\leq}Q_f{\leq}1$. $P{\acute{o}}lya$-Knopp's inequality is also refined by the similar form.

• 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.

• Honam Mathematical Journal
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• v.44 no.4
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• pp.513-520
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• 2022

The Jensen and Mercer inequalities are very important inequalities in information theory. The article provides the generalization of Mercer's inequality for convex functions on the line segments. This result contains Mercer's inequality as a particular case. Also, we investigate bounds for Shannon's entropy and give some new applications in zeta function and analysis.

• Journal of the Korean Mathematical Society
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• v.50 no.3
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• pp.465-477
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• 2013

In this paper, two different methods of proving Jensen's inequality on time scales for superquadratic functions are demonstrated. Some refinements of classical inequalities on time scales are obtained using properties of superquadratic functions and some known results for isotonic linear functionals.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1373-1381
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• 2007

In this paper, we establish an equivalence form of the Brunn-Minkowski inequality for volume differences. As an application, we obtain a general and strengthened form of the dual $Kneser-S\ddot{u}ss$ inequality.

• Journal of the Korean Mathematical Society
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• v.32 no.3
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• pp.493-507
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• 1995

The Hartman-Stampacchia variational inequality was first suggested and studied by Hartman and Stampacchia [8] in finite dimensional spaces during the time establishing the base of variational inequality theory in 1960s [4]. Then it was generalized by Lions et al. [6], [9], [10], Browder [3] and others to the case of infinite dimensional inequality [3], [9], [10], and the results concerning this variational inequality have been applied to many important problems, i.e., mechanics, control theory, game theory, differential equations, optimizations, mathematical economics [1], [2], [6], [9], [10]. Recently, the Browder-Hartman-Stampaccnia variational inequality was extended to the case of set-valued monotone mappings in reflexive Banach sapces by Shih-Tan [11] and Chang [5], and under different conditions, they proved some existence theorems of solutions of this variational inequality.

• 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.