• Title, Summary, Keyword: inequality

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FRACTIONAL GAGLIARDO-NIRENBERG INEQUALITY

  • Park, Young Ja
    • Journal of the Chungcheong Mathematical Society
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    • v.24 no.3
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    • pp.583-586
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    • 2011
  • A fractional Gagliardo-Nirenberg inequality is established. A sharp fractional Sobolev inequality is discussed as a direct consequence.

Perception of Inequality and Societal Health: Analysis on Social Trust and Social Mobility

  • Hwang, Sun-Jae
    • Asian Journal for Public Opinion Research
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    • v.6 no.1
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    • pp.1-17
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    • 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.

APPLICATIONS OF TAYLOR SERIES FOR CARLEMAN'S INEQUALITY THROUGH HARDY INEQUALITY

  • IDDRISU, MOHAMMED MUNIRU;OKPOTI, CHRISTOPHER ADJEI
    • Korean Journal of Mathematics
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    • v.23 no.4
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    • pp.655-664
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    • 2015
  • In this paper, we prove the discrete Hardy inequality through the continuous case for decreasing functions using elementary properties of calculus. Also, we prove the Carleman's inequality through limiting the discrete Hardy inequality with applications of Taylor series.

Improved Carleman's Inequality and Improvement of Polya-Knopp's Inequality (칼레만 부등식의 개선 결과들과 폴야-놉 부등식의 개선)

  • Kwon, Ern Gun;Lee, Jinkee
    • East Asian mathematical journal
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    • v.34 no.4
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    • pp.359-369
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    • 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.

Stability of Time-delayed Linear Systems with New Integral Inequality Proportional to Integration Interval (새로운 적분구간 비례 적분 부등식을 이용한 시간지연 선형시스템의 안정성)

  • Kim, Jin-Hoon
    • 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.

INEQUALITIES FOR DUAL HARMONIC QUERMASSINTEGRALS

  • Jun, Yuan;Shufeng Yuan;Gangsong Leng
    • Journal of the Korean Mathematical Society
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    • v.43 no.3
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    • pp.593-607
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    • 2006
  • In this paper, we study the properties of the dual harmonic quermassintegrals systematically and establish some inequalities for the dual harmonic quermassintegrals, such as the Minkowski inequality, the Brunn-Minkowski inequality, the Blaschke-Santalo inequality and the Bieberbach inequality.

MIXED CHORD-INTEGRALS OF STAR BODIES

  • Fenghong, Lu
    • Journal of the Korean Mathematical Society
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    • v.47 no.2
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    • pp.277-288
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    • 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.

ON HEINZ-KATO-FURUTA INEQUALITY WITH BEST BOUNDS

  • Lin, C.S.
    • 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].

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