• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.275-283
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• 2013

In this paper we investigate an initial boundary value problem of a logarithmic wave equation. We establish the global existence of weak solutions to the problem by using Galerkin method, logarithmic Sobolev inequality and compactness theorem.

• Journal of the Chungcheong Mathematical Society
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• v.26 no.1
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• pp.105-110
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• 2013

A logarithmic composition inequality in Besov spaces is derived which generalizes Vishik's inequality: ${\parallel}f{\circ}g{\parallel}_{B^s_{p,1}}{\leq}(1+{\log}({\parallel}{\nabla}g{\parallel}_{L^{\infty}}{\parallel}{\nabla}g^{-1}{\parallel}_{L^{\infty}})){\parallel}f{\parallel}_{B^s_{p,1}}$, where $g$ is a volume-preserving diffeomorphism on ${\mathbb{R}}^n$.

• East Asian mathematical journal
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• v.34 no.1
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• pp.17-20
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• 2018

Hardy-Bennett inequality is an inequality of Hardy-type having logarithmic weight. It appeared in 1973, and several generalizations followed. We, in this note, present another generalization with a simple proof.

• Honam Mathematical Journal
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• v.21 no.1
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• pp.127-137
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• 1999

An inequality of Ostrowski type for twice differentiable mappings whose derivatives belong to $L_{1}(a,\;b)$ and applications in Numerical Integration and for special means (logarithmic mean, identric mean, p-logarithmic mean etc...) are given.

• The Pure and Applied Mathematics
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• v.15 no.4
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• pp.387-392
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• 2008

In this note, an alternative proof and extensions are provided for the following conclusions in [6, Theorem 1 and Theorem 3]: The functions $\frac1{x^2}-\frac{e^{-x}}{(1-e^{-x})^2}\;and\;\frac1{t}-\frac1{e^t-1}$ are decreasing in (0, ${\infty}$) and the function $\frac{t}{e^{at}-e^{(a-1)t}}$ for a $a{\in}\mathbb{R}\;and\;t\;{\in}\;(0,\;{\infty})$ is logarithmically concave.

• Bulletin of the Korean Mathematical Society
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• v.59 no.6
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• pp.1495-1510
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• 2022

This paper aims to investigate the initial boundary value problem of the nonlinear viscoelastic Petrovsky type equation with nonlinear damping and logarithmic source term. We derive the blow-up results by the combination of the perturbation energy method, concavity method, and differential-integral inequality technique.

• Korean Journal of Social Welfare
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• v.64 no.2
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• pp.55-83
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• 2012

Self-employment rate is high in Korean labor market, while the income gap within self-employed is also high. Although, there are very few studies that addressed on the income inequality of self-employed. Thus, this study has measured the earnings inequality of self-employed by generalized entropy indices and decomposed inequality factor and trend. The empirical study is based on Korea Welfare Panel Study wave 1~4. The main result from this analysis is summarized in three points. Firstly, earnings inequality of self-employed is severely high and the earnings polarization within self-employed has become more serious in Korea. Secondly, this study provides the evidence that the main factor of earnings inequality of self-employed is the status of self-employment, education level, age group, workplace scale and industry. Thirdly, the contribution of relative changes in the incomes of the status of self-employment is the largest to the inequality trend. In terms of education level, age group and industry, the increase of inequality within group(pure effect) mainly attributes to the rise of earnings inequality of self-employed and the change effect of group composition contributes to deterioration of inequality.

• Korean Journal of Social Welfare
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• v.61 no.2
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• pp.391-415
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• 2009

The purpose of this study is to examine the trends of income inequality by gender since 1997 economic crisis and to investigate what is the most influential factor on these changes for males and females. Data used for this study are nine waves of Korean Labor and Income Panel Study(KLIPS). Income inequality is measured by the Gini coefficient and the mean logarithmic deviation(MLD) and the MLDs are decomposed into three components to quantify within- and between-group inequalities. The results show that the extent of income inequality is greater for women during the whole period and is fluctuated more widely. Women's income inequality is mainly affected by the family-related variables, such as age and marital status, while men's inequality is primarily determined by the labor market factors, such as employment status, industrial types and occupation status. These results imply that gender-sensetive welfare policies need to be implemented and that it is necessary to assist the poor women and men through the benefits from the income assistance programs and labor market programs.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.2
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• pp.183-186
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• 2008

We consider fuzzy invex sets, fuzzy preinvex functions, fuzzy quasi-preinvex functions, and fuzzy logarithmic preinvex functions. Murofushi et al. have been studied Choquet integrals and their properties. In this paper, we study some characterizations in Choquet integrals as follows: fuzzy preinvexity, fuzzy quasi-preinvexity, and fuzzy logarithemic preinvexity, that mean some characterizations of functionals defined by Choquet integrals. Furthermore, we discuss Jensen's type inequality in Choquet integrals.

• Bulletin of the Korean Mathematical Society
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• v.49 no.1
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• pp.33-47
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• 2012

In this paper, the log-convexity of another class one-parameter mean is investigated. As applications, some new upper and lower bounds of logarithmic mean, new estimations for identric mean and new inequalities for power-exponential mean and exponential-geometric mean are first given.