• East Asian mathematical journal
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• v.21 no.1
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• pp.41-48
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• 2005

In this paper we first introduce a space of homogeneous type X, and then consider a kind of generalized upper half-space $X{\times}(0,\;\infty)$. We are mainly considered with inequalities for the $L^p$ norms of area functions associated with approach regions in $X{\times}(0,\;\infty)$.

• Communications of the Korean Mathematical Society
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• v.29 no.2
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• pp.263-267
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• 2014

We study the growth rate of $H^1$ Sobolev norm of the solutions to Gross-Neveu and Thirring equations. A well-known result is the double exponential rate. We show that the $H^1$ Sobolev norm grows at most an exponential rate exp($ct^2$).

• Honam Mathematical Journal
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• v.42 no.3
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• pp.569-576
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• 2020

An element x ∈ E is called a norming point of P ∈ P(ⁿE) if ║x║ = 1 and |P(x)| = ║P║. For P ∈ P(ⁿE), we define Norm(P) = {x ∈ E : x is a norming point of P}. Norm(P) is called the norming set of P. We classify Norm(P) for P ∈ 𝒫(²𝑙²_∞).

• Bulletin of the Korean Mathematical Society
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• v.53 no.1
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• pp.247-262
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• 2016

We propose and analyze spectral and pseudo-spectral Jacobi-Galerkin approaches for weakly singular Volterra integral equations (VIEs). We provide a rigorous error analysis for spectral and pseudo-spectral Jacobi-Galerkin methods, which show that the errors of the approximate solution decay exponentially in $L^{\infty}$ norm and weighted $L^2$-norm. The numerical examples are given to illustrate the theoretical results.

• East Asian mathematical journal
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• v.31 no.5
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• pp.685-693
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• 2015

In this paper, we introduce fully discrete mixed discontinuous Galerkin approximations for parabolic problems. And we analyze the error estimates in $l^{\infty}(L^2)$ norm for the primary variable and the error estimates in the energy norm for the primary variable and the flux variable.

• Journal of applied mathematics & informatics
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• v.7 no.1
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• pp.61-82
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• 2000

In this paper two so-called regularized Green's functions are introduced to derive the optimal maximum norm error estimates for the unknown function and the adjoint vector-valued function for mixed finite element methods of Laplacian operator. One contribution of the paper is a demonstration of how the boundedness of $L^1$-norm estimate for the second Green's function ${\lambda}_2$ and the optimal maximum norm error estimate for the adjoint vector-valued function are proved. These results are seemed to be to be new in the literature of the mixed finite element methods.

• 제어로봇시스템학회:학술대회논문집
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• 1996.10a
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• pp.64-68
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• 1996

In this note, we propose the discrete model reduction method over disc-type analytic domains. We define Hankel singular value over the disc that is mapped by standard bilinear mapping. And GSPA(generalized singular perturbation approximation) and DT(direct truncation) are generalized to GSPA and DT over a disc. Furthermore we show that the reduced order model over a smaller domain has a smaller L$_{\infty}$ norm error bound..

• Korean Journal of Mathematics
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• v.31 no.3
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• pp.305-311
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• 2023

We exhibit some properties of the weighted Berezin transform T_αf on L^∞(B_n) and on L¹(B_n). As the main result, we prove that if f ∈ L^∞(B_n) with lim_k→∞ T^k_αf exists, then there exist unique M-harmonic function g and $h{\in}{\bar{(I-T_{\alpha})L^{\infty}(B_n)}}$ such that f = g + h. We also show that of the norm of weighted Berezin operator T_α on L¹(B_n, ν) converges to 1 as α tends to infinity, where ν is an ordinary Lebesgue measure.

• Journal of the Institute of Electronics Engineers of Korea SC
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• v.40 no.2
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• pp.10-18
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• 2003

This paper presents a method for designing guaranteed cost fuzzy filter with a desired H$_{\infty}$ disturbance rejection constraint of delayed fuzzy dynamic systems. This method not only guarantees an induced L$_2$ norm bound constraint on disturbance attenuation, but also minimizes an upper bound on a linear quadratic performance measure. A sufficient condition for the existence of guaranteed cost fuzzy filter with H$_{\infty}$ constraint is then presented in terms of linear matrix inequalities(LMIs). A simulation example is given to illustrate the design procedures and performances of the proposed methods.

• Kyungpook Mathematical Journal
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• v.60 no.3
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• pp.485-505
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• 2020

We present a complete description of all the extreme points of the unit ball of 𝓛_s(²𝑙³_∞) which leads to a complete formula for ║f║ for every f ∈ 𝓛_s(²𝑙³_∞)^∗. We also show that $extB_{{\mathcal{L}}_s(^2l^3_{\infty})}{\subset}extB_{{\mathcal{L}}_s(^2l^n_{\infty})}$ for every n ≥ 4. Using the formula for ║f║ for every f ∈ 𝓛_s(²𝑙³_∞)^∗, we show that every extreme point of the unit ball of 𝓛_s(²𝑙³_∞) is exposed. We also characterize all the smooth points of the unit ball of 𝓛_s(²𝑙³_∞).