• 대한수학회논문집
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• 제24권2호
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• pp.187-195
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• 2009

We investigate the boundary values of the holomorphic mean Lipschitz function. In fact, we prove that the admissible limit exists at every boundary point of the unit ball for the holomorphic mean Lipschitz functions under some assumptions on the Lipschitz order. Moreover, we get embedding theorems of holomorphic mean Lipschitz spaces into Hardy spaces or into the Bloch space on the unit ball in $\mathbb{C}_n$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제21권1호
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• pp.11-21
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• 2014

The present paper is concerned with the notions of Lipschitz and asymptotic stability for perturbed nonlinear differential system knowing the corresponding stability of nonlinear differential system. We investigate Lipschitz and asymtotic stability for perturbed nonlinear differential systems. The main tool used is integral inequalities of the Bihari-type, in special some consequences of an extension of Bihari's result to Pinto and Pachpatte, and all that sort of things.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권1호
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• pp.1-11
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• 2015

The present paper is concerned with the notions of Lipschitz and asymptotic for perturbed functional differential system knowing the corresponding stability of functional differential system. We investigate Lipschitz and asymptotic stability for perturbed functional differential systems. The main tool used is integral inequalities of the Bihari-type, and all that sort of things.

• Kyungpook Mathematical Journal
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• 제60권1호
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• pp.117-125
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• 2020

In this paper, we first introduce new classes of Lipschitz algebras of infinitely differentiable functions which are extensions of the standard Lipschitz algebras of infinitely differentiable functions. Then we determine the maximal ideal space of these extended algebras. Finally, we show that if X and K are uniformly regular subsets in the complex plane, then R(X, K) is natural.

• 충청수학회지
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• 제26권4호
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• pp.831-842
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• 2013

In this paper, we investigate uniform Lipschitz and asymptotic stability for perturbed differential systems using integral inequalities.

• 대한수학회지
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• 제34권4호
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• pp.959-971
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• 1997

In the paper we introduce Hausdorff measures which are suitable or the study of Lipschitz regularity of M-harmonic function in the unit ball B in $C^n$. For an M-harmonic function h which satisfies certain integrability conditions, we show that there is an open set $\Omega$, whose Hausdorff content is arbitrarily small, such that h is Lipschitz smooth on $B \backslash \Omega$.

• Korean Journal of Mathematics
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• 제16권1호
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• pp.85-90
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• 2008

We consider Fourier multiplier operators whose symbols satisfy a generalization of $H{\ddot{o}}rmander^{\prime}s$ condition and establish their Sobolev-type mapping properties on the homogeneous Besov-Lipschitz spaces by making use of a continuous characterization of Besov-Lipschitz spaces. As an application, we derive Sobolev-type imbedding theorem.

• Journal of applied mathematics & informatics
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• 제33권1_2호
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• pp.219-228
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• 2015

In this paper, we investigate Lipschitz and asymptotic stability for perturbed functional differential systems.

• Korean Journal of Mathematics
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• 제23권1호
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• pp.181-197
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• 2015

In this paper, we investigate Lipschitz and asymptotic stability for perturbed nonlinear differential systems.

• 충청수학회지
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• 제27권4호
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• pp.591-602
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• 2014

In this paper, we investigate Lipschitz and asymptotic stability for nonlinear perturbed differential systems.