• Journal of Institute of Control, Robotics and Systems
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• v.14 no.8
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• pp.837-841
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• 2008

This paper presents a robust reduced order state observer for a class of Lipschitz nonlinear systems with external disturbance. Sufficient conditions on the existence of the proposed observer are characterized by linear matrix inequalities. It is also shown that the proposed observer design can reduce the effect on the estimation error of external disturbance up to the prescribed level. Finally, a numerical example is provided to verify the proposed design method.

• Journal of the Chungcheong Mathematical Society
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• v.29 no.3
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• pp.429-442
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• 2016

In this paper we show that the solutions to the perturbed differential system $$y^{\prime}=f(t,y)+{\int}_{to}^{t}g(s,y(s),Ty(s))ds$$ have uniformly Lipschitz stability and asymptotic behavior by imposing conditions on the perturbed part $\int_{to}^{t}g(s,y(s),Ty(s))ds$ and the fundamental matrix of the unperturbed system y' = f(t, y).

• Honam Mathematical Journal
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• v.22 no.1
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• pp.21-30
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• 2000

Lipschitz Algebras Lip(X, ${\alpha}$) and lip(X, ${\alpha}$) were first studied by D. R. Sherbert in 1964. B. Pavlovic in 1995 shown that in these algebras, the prime ideals containing a given prime ideal form a chain. In this paper, we show that the above property holds in $Lip^n(X,\;{\alpha})$ and $lip^n(X,\;{\alpha})$, the Lipschitz algebras of finite differentiable functions on a perfect compact place set X.

• Journal of the Korean Mathematical Society
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• v.44 no.4
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• pp.931-940
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• 2007

Holomorphic mean Lipschitz space is defined in the unit ball of $\mathbb{C}^n$. The membership of the space is expressed in terms of the growth of radial derivatives, which reduced to a classical result of Hardy and Littlewood when n = 1. The membership is also expressed in terms of the growth of tangential derivatives when $n{\ge}2$.

• Journal of the Korean Mathematical Society
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• v.59 no.3
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• pp.469-494
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• 2022

In this paper, we study the boundedness of a class of inhomogeneous Journé's product singular integral operators on the inhomogeneous product Lipschitz spaces. The consideration of such inhomogeneous Journé's product singular integral operators is motivated by the study of the multi-parameter pseudo-differential operators. The key idea used here is to develop the Littlewood-Paley theory for the inhomogeneous product spaces which includes the characterization of a special inhomogeneous product Besov space and a density argument for the inhomogeneous product Lipschitz spaces in the weak sense.

• Communications of the Korean Mathematical Society
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• v.11 no.4
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• pp.975-981
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• 1996

Let $D \subset C^2$ be a bounded convex domain with real analytic boundary. We get some Lipschitz regularity of the Cauchy transform on the convex domain D.

• Kyungpook Mathematical Journal
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• v.47 no.2
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• pp.253-265
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• 2007

In this paper, the boundedness for some multilinear operators generated by singular integralv operators and Lipschitz functions on Hardy and Herz-type spaces are obtained.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.273-280
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• 2006

Lipschitzian semigroup is a semigroup of Lipschitz operators which contains $C_0$ semigroup and nonlinear semigroup. In this paper, we establish the cannonical exponential formula of Lipschitzian semigroup from its Lie generator and the approximation theorem by Laplace transform approach to Lipschitzian semigroup.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.1-17
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• 2004

The famous Newton-Kantorovich hypothesis has been used for a long time as a sufficient condition for the convergence of Newton method to a solution of an equation in connection with the Lipschitz continuity of the Frechet-derivative of the operator involved. Using Lipschitz and center-Lipschitz conditions we show that the Newton-Kantorovich hypothesis is weakened. The error bounds obtained under our semilocal convergence result are finer and the information on the location of the solution more precise than the corresponding ones given by the dominating Newton-Kantorovich theorem, and under the same hypotheses/computational cost, since the evaluation of the Lipschitz also requires the evaluation of the center-Lipschitz constant. In the case of local convergence we obtain a larger convergence radius than before. This observation is important in computational mathematics and can be used in connection to projection methods and in the construction of optimum mesh independence refinement strategies.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.27 no.10A
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• pp.1011-1020
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• 2002

The current paper presents an effective deblocking algorithm for block-based coded images using singularity detection in a wavelet transform. In block-based coded images, the local maxima of a wavelet transform modulus detect all singularities, including blocking artifacts, from multiscale edges. Accordingly, the current study discriminates between a blocking artifact and an edge by estimation the Lipschitz regularity of the local maxima and removing the wavelet transform modulus of a blocking artifact that has a negative Lipschitz regularity exponent. Experimental results showed that the performance of the proposed algorithm was objectively and subjectively superior.