• The Pure and Applied Mathematics
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• v.14 no.1 s.35
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• pp.7-14
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• 2007

The aim of this paper is to study the superstability problem of the cosine type functional equation f(x+y)+f(x+${\sigma}y$)=2g(x)g(y).

• Bulletin of the Korean Mathematical Society
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• v.46 no.2
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• pp.295-301
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• 2009

We prove the Hyers-Ulam stability of a Pexiderized exponential equation of mappings f, g, h : $G{\times}S{\rightarrow}{\mathbb{C}}$, where G is an abelian group and S is a commutative semigroup which is divisible by 2. As an application we obtain a stability theorem for Pexiderized exponential equation in Schwartz distributions.

• Journal of the Korean Mathematical Society
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• v.37 no.5
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• pp.763-777
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• 2000

We investigate the existence of group invariant solutions of the Emden-Fowler equation, - u=$\mid$x$\mid$$\sigma$$\mid$u$\mid$p-1u in B, u=0 on B and u(gx)=u(x) in B for g G. Here B is the unit ball in n 2, 1$\sigma$ 0 and G is a closed subgrop of the orthogonal group. A soultion of the problem is called a G in variant solution. We prove that there exists a G invariant non-radial solution if and only if G is not transitive on the unit sphere.

• Korean Journal of Mathematics
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• v.29 no.4
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• pp.765-774
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• 2021

In this paper, we solve and investigate the superstability of the p-radical functional equations $$f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}f(x)g(y),\\f(\sqrt[p]{x^p+y^p})-f(\sqrt[p]{x^p-y^p})={\lambda}g(x)f(y),$$ which is related to the trigonometric(Kim's type) functional equations, where p is an odd positive integer and f is a complex valued function. Furthermore, the results are extended to Banach algebras.

• Communications of the Korean Mathematical Society
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• v.20 no.4
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• pp.775-779
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• 2005

On a compact n-dimensional manifold $M^n$, a critical point of the total scalar curvature functional, restricted to the space of metrics with constant scalar curvature of volume 1, satifies the critical point equation (CPE), given by $Z_g\;=\;s_g^{1\ast}(f)$. It has been conjectured that a solution (g, f) of CPE is Einstein. The purpose of the present paper is to prove that every compact stable minimal hypersurface is in a certain hypersurface of $M^n$ under an assumption that Ker($s_g^{1\ast}{\neq}0$).

• Communications of the Korean Mathematical Society
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• v.20 no.1
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• pp.93-106
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• 2005

In this paper, we obtain the generalization of the Hyers-Ulam-Rassias stability in the sense of Gavruta and Ger of the generalized G-type functional equations of the form $f({{\varphi}(x)) = {\Gamma}(x)f(x)$. As a consequence in the cases ${\varphi}(x) := x+p:= x+1$, we obtain the stability theorem of G-functional equation : the reciprocal functional equation of the double gamma function.

• Bulletin of the Korean Mathematical Society
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• v.43 no.4
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• pp.679-692
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• 2006

On a compact oriented n-dimensional manifold $(M^n,\;g)$, it has been conjectured that a metric g satisfying the critical point equation (2) should be Einstein. In this paper, we prove that if a manifold $(M^4,\;g)$ is a 4-dimensional oriented compact warped product, then g can not be a solution of CPE with a non-zero solution function f.

• The Pure and Applied Mathematics
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• v.23 no.3
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• pp.265-285
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• 2016

In this paper, we introduce functional equations in G-normed spaces and we prove the Hyers-Ulam stability of an additive-quadratic-cubic-quartic functional equation in complete G-normed spaces by using the fixed point method.

• Honam Mathematical Journal
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• v.28 no.3
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• pp.409-415
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• 2006

On a compact oriented smooth 3-dimensional manifold (M, g), we consider the critical point equation(CPE) defined as $z_g=s^{{\prime}*}_g(f)$. Under CPE, it is shown in [5] that every stable minimal hypersurface in M is contained in ${\varphi}^{-1}(0)$ for ${\varphi}{\in}$ ker $s^{{\prime}*}_g$. We study analytic and geometric conditions under which the stable minimal hypersurface in M does not exist.

• Journal of Preventive Medicine and Public Health
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• v.28 no.1 s.49
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• pp.73-84
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• 1995

This study was conducted to measure the lead level in the blood, scalp hair and toenail of the elementary schoolchildren and assess the relationship among those samples. Lead concentration of the blood, scalp hair and toenail was measured for 100(male 50, female 50) fourth grade elementary schoolchildren in Taegu city. The mean lead level in the blood, scalp hair and toenail was $6.00{\pm}2.44{\mu}g/dl,\;6.68{\pm}3.54{\mu}g/g,\;and\;7.33{\pm}3.18{\mu}g/g. The mean lead level in the blood of schoolboys was $6.43{\pm}2.77{\mu}g/dl$, and that of schoolgirls was $5.59{\pm}2.01{\mu}g/dl$. The mean lead level in the scalp hair of schoolboys was $7.66{\pm}2.97{\mu}g/g$ and that of schoolgirls was $6.88{\pm}3.54{\mu}g/g$. The mean lead level in the toenail of schoolboys was $8.19{\pm}3.5{\mu}g/g$ and that of schoolgirls was $6.47{\pm}2.52{\mu}g/g$ and their difference was statistically significant. In schoolboys, the correlation coefficient between the lead level in the blood and scalp hair was 0.4909, and the data were fitted best by the regression equation Y = 0.5255X+4. 2810, where Y and X are scalp hair and blood concentration. In schoolgirls the correlation coefficient between the lead level in the blood and scalp hair was 0.3778, and the data were fitted best by the regression equation Y = 0.6655X+2.9632, where Y and X are scalp hair and blood concentration. In schoolboys, the correlation coefficient between the lead level in the blood and in the toenail was 0.5533, and the data were fitted best by the regression equation Y = 0.7076X+3. 6472, where Y and X are toenail and blood concentration. In schoolgirls the correlation coefficient between the lead level in the blood and in the toenail was 0.2738, and the data were fitted best by the regression equation Y = 0.3431X+4.5570, where Y and X are toenail and blood concentration In schoolboys, the correlation coefficient between the lead level in the scalp hair and in the toenail, in the schoolboys was 0.4148, and the data were fitted best by the regression equation Y = 0.4956X+4.3986, where Y and X are toenail and scalp hair concentration. In schoolgirls, the correlation coefficient between the lead level in the scalp hair and in the toenail was 0.1159, and the data were fitted best by the regression equation Y = 0.0825X+5. 9214, where Y and X are toenail and scalp hair concentration. Correlation among lead concentration in the blood, scalp hair and toenail of schoolchildren were statistically significant except between scalp hair and toenail in schoolgirls. These finding suggest that blood, scalp hair and toenail can be used as substitutive samples between each others.