• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.3
• /
• pp.321-324
• /
• 2018

We present a new and simple proof of improved Carleson's inequality.

• Journal of the Chungcheong Mathematical Society
• /
• v.24 no.3
• /
• pp.583-586
• /
• 2011

A fractional Gagliardo-Nirenberg inequality is established. A sharp fractional Sobolev inequality is discussed as a direct consequence.

• Journal of the Korean Society for Library and Information Science
• /
• v.55 no.2
• /
• pp.263-287
• /
• 2021

Researches on inequality in Korean society has been sporadically conducted in various areas. In this study, research trend related to inequality was analyzed through basic statistical analysis, co-occurrence analysis, and main path analysis using articles related to inequality from Korea citation index. In basic statistical analysis, key authors, journals, and articles are identified. In co-occurrence analysis, income inequality, educational inequality, welfare inequality, and policy on inequality were identified as main topics. Main path analysis showed two research trends after 2004. One was research trend on economic inequality, and the other was on health inequality and social structural inequality.

• East Asian mathematical journal
• /
• v.34 no.4
• /
• pp.359-369
• /
• 2018

This note, we first show that the famous Carleman's inequality can be improved if we find a positive sequence $\{c_n\}$ such that $c_n{\sum\limits_{j=n}^{\infty}}{\frac{1}{j\(\prod_{k=1}^{j}ck\)^{\frac{1}{j}}}}$ < e. Then we list a lot of known results in the literature improving Carleman's inequality by this method. These results can be a good source to a further research for interested students. We next consider about similar improvement of Polya-Knopp's inequality, which is a continuous version of Carleman's inequality. We show by a manner parallel to the case of Carleman's inequality that Polya-Knopp's inequality can be improved if we find a positive function c(x) such that $c(x){\int}_{x}^{\infty}\frac{1}{t\;{\exp}\(\frac{1}{t}{\int}_{0}^{t}{\ln}\;c(s)\;ds\)}dt$ < e. But there are no known results improving Polya-Knopp's inequality by this method. Suggesting to find a new method, we lastly show that there is no nice continuous function c(x) that satisfies the inequality.

• Asian Journal for Public Opinion Research
• /
• v.6 no.1
• /
• pp.1-17
• /
• 2018

As societal interest in inequality increases in Korea, both public and academic discussion on inequality is also on the rise. In order to more effectively discuss the problems of rising inequality, however, it is essential to study the consequences and implications of inequality. This study examines one of the consequences of inequality, particularly on individuals - the relationship between an individual's perception of inequality and his/her evaluation of societal health, such as social trust and social mobility. According to a statistical analysis of the Korean Academic Multimode Open Survey for Social Sciences (KAMOS), those who perceive the level of income and wealth inequality in Korea as more unequal tend to have a lower level of trust toward Korean society and Korean people, as well as a lower expectation for both intra- and intergenerational social mobility. This study, which shows that rising inequality could have a negative impact at the individual level, not only extends the scope of the consequence-of-inequality studies from the society-oriented toward the individual-oriented, but it also has significant implications for the field, suggesting a new direction for future studies.

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

• Journal of the Korean Mathematical Society
• /
• v.47 no.2
• /
• pp.277-288
• /
• 2010

The mixed chord-integrals are defined. The Fenchel-Aleksandrov inequality and a general isoperimetric inequality for the mixed chordintegrals are established. Furthermore, the dual general Bieberbach inequality is presented. As an application of the dual form, a Brunn-Minkowski type inequality for mixed intersection bodies is given.

• The Pure and Applied Mathematics
• /
• v.19 no.3
• /
• pp.305-313
• /
• 2012

In this note we study Nesbitt's Inequality and modify it to make several inequalities. We prove some inequalities by using power series and Cauchy-Schwarz Inequality.

• The Transactions of The Korean Institute of Electrical Engineers
• /
• v.65 no.3
• /
• pp.457-462
• /
• 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
• /
• v.23 no.1
• /
• pp.137-147
• /
• 2010

In this paper we extend a differential inequality presented in Theorem 2.2 [6] to a dynamic inequality on time scales.