• Journal of the Korean Mathematical Society
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• v.39 no.5
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• pp.709-729
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• 2002

Using the well known Hermite-Hadamard integral inequality for convex functions, some inequalities for the finite Hilbert transform of functions whose first derivatives are convex are established. Some numerical experiments are performed as well.

• Journal of the Korean Mathematical Society
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• v.40 no.2
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• pp.207-224
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• 2003

Some weighted Ostrowski type integral inequalities for vector-valued functions in Hilbert spaces are given. Applications for quadrature rules with values in Hilbert spaces are also pointed out.

• Journal of applied mathematics & informatics
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• v.18 no.1_2
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• pp.685-689
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• 2005

We find some Hilbert functions of codimension 4, which are obtained from only k-configurations in $\mathbb{P}^{3}$ and support the $3^{rd}$ linear syzygy.

• Journal of the Korean Mathematical Society
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• v.57 no.3
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• pp.777-792
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• 2020

We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information about lex segment ideals. Moreover, we introduce numerical functions called fractal functions, and we use them to solve the open problem of the classification of the Hilbert functions of any bigraded algebra.

• Korean Journal of Mathematics
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• v.31 no.2
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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.

• Honam Mathematical Journal
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• v.38 no.3
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• pp.495-506
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• 2016

In this paper, we introduce and investigate a new subclass of meromorphic functions associated with a certain integral operator on Hilbert space. For this class, we obtain several properties like the coefficient inequality, extreme points, radii of close-to-convexity, starlikeness and meromorphically convexity and integral transformation. Further, it is shown that this class is closed under convex linear combination.

• Korean Journal of Mathematics
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• v.24 no.2
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• pp.273-296
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• 2016

Some new trace inequalities for convex functions of self-adjoint operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated. Some trace inequalities for matrices are also derived. Examples for the operator power and logarithm are presented as well.

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.39-57
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• 2003

Some inequalities for the Hilbert transform of the product of two functions are given.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.543-559
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• 2002

Some inequalities and approximations for the finite filbert transform by the use of Ostrowski type inequalities for absolutely continuous functions are given.

• Journal of applied mathematics & informatics
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• v.17 no.1_2_3
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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.