• Journal of applied mathematics & informatics
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• 제17권1_2_3호
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• pp.567-572
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• 2005

A Banach space X is a Hilbert space if and only if $$E{\mid}x=Y{\mid}{\le}2$$ for all x$\in$ X and all X-valued Bochner integrable functions Y satisfying EY = 0 and ${\mid}x-Y{\mid}{\le}2$ a.e.

• Kyungpook Mathematical Journal
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• 제46권3호
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• pp.425-431
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• 2006

In this paper, by introducing three parameters A, B and ${\lambda}$, and estimating the weight coefficient, we give a new extension of Hardy-Hilbert's inequality with a best constant factor, involving the Beta function. As applications, we consider its equivalent inequality.

• Journal of applied mathematics & informatics
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• 제16권1_2호
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• pp.533-537
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• 2004

A Banach space X is a Hilbert space if and only if E｜x + Y｜$geq$ 1 for all x $\epsilon$ X and all X-valued Bochner integrable functions Y satisfying EY = 0 and ｜Y｜$geq$ 1 a.e.

• Kyungpook Mathematical Journal
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• 제52권3호
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• pp.291-298
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• 2012

In this paper, by estimating the weight function, we give a new Hilbert-type inequality with the integral in whole plane. As its applications, we consider the equivalent and a particular result.

• 충청수학회지
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• 제23권4호
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• pp.699-704
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• 2010

In this paper, we prove that the Hilbert 2-class field tower of an imaginary quadratic function field $F=k({\sqrt{D})$ is infinite if $r_2({\mathcal{C}}(F))=4$ and exactly one monic irreducible divisor of D is of odd degree, except for one type of $R{\acute{e}}dei$ matrix of F. We also compute the density of such imaginary quadratic function fields F.

• Kyungpook Mathematical Journal
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• 제50권2호
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• pp.281-288
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• 2010

By introducing some parameters and using the way of weight function and the technic of real analysis and complex analysis, a new Hilbert-type integral inequality with a best constant factor and a combination kernel involving two mean values is given, which is an extension of Hilbert's integral inequality. As applications, the equivalent form and the reverse forms are considered.

• Korean Journal of Mathematics
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• 제31권2호
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• pp.189-201
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• 2023

In this article, we establish Hilbert-type integral inequalities with the help of a non-homogeneous kernel of hyperbolic function with best constant factor. We also study the obtained inequalities's equivalent form. Additionaly, several specific Hilbert's type inequalities with constant factors in the term of the rational fraction expansion of higher order derivatives of cotangent and cosine functions are presented.

• 충청수학회지
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• 제28권4호
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• pp.537-543
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• 2015

In [9], the authors determine an infinite class of non-unimodal Gorenstein sequence, which includes the example $$\bar{h}_1\text{ = (1, 125, 95, 77, 71, 77, 95, 125, 1)}$$. They raise a question whether there is a Gorenstein algebra with Hilbert function $$\bar{h}_2\text{= (1, 125, 95, 77, 70, 77, 95, 125, 1)}$$, which has remained an open question. In this paper, we prove that there is no Gorenstein algebra with Hilbert function $\bar{h}_2$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제27권1호
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• pp.1-11
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• 2020

In this paper we determine conditions which a function a(t) must satisfy to insure that the function a'(t) is an element of the separable Hilbert space L²_a,b[0, T]. We then proceed to illustrate our results with several pertinent examples and counter-examples.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권2호
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• pp.79-87
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• 2013

In this paper we study the infniteness of Hilbert 2-class field towers of inert imaginary quadratic function fields over $\mathbb{F}_q(T)$, where $q$ is a power of an odd prime number.