• 대한수학회지
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• 제34권1호
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• pp.195-211
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• 1997

The purpose of this paper is to present the uniform asymptotic stability theorem and the uniform boundedness and uniform ultimate boundedness theorem for functional differential equations.

• 대한수학회지
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• 제40권2호
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• pp.307-317
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• 2003

For linear operators between Banach algebras "spectral boundedness" is derived from ordinary boundedness by substituting spectral radius for norm. The interplay between this concept and some of its near relatives is conspicuous in a result of Curto and Mathieu.

• Journal of applied mathematics & informatics
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• 제18권1_2호
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• pp.261-272
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• 2005

In this paper, boundedness criteria are established for solutions of a class of impulsive functional differential equations with infinite delays of the form $x'(t) = F(t, x(\cdot)), t > t^{\ast} {\Delta}x(t_{k})= I(t_{k}, x(t_{k}^{-})), k = 1,2,...$ By using Lyapunov functions and Razumikhin technique, some new Razumikhin-type theorems on boundedness are obtained.

• 한국산업정보학회논문지
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• 제9권4호
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• pp.75-79
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• 2004

We investigate various $\phi_0-boundedness$ and $\phi_0-Lagrange$ stability of the trivial solution of comparison differential system. We also investigated the corresponding boundedness concepts of the trivial solution of the differential system using the theory of differential inequalities through cones and the method of cone valued Lyapunov functions.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.1-5
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• 1996

A strong Banach-Mackey property is established for ${\kappa}$-spaces including all complete and some non-complete metric linear spaces and some non-metrizable locally convex spaces. As applications of this result, a strong uniform boundedness result and a new Banach-Steinhaus type theorem are obtained.

• 충청수학회지
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• 제20권3호
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• pp.287-296
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• 2007

Using the representation of the solution by means of the resolvent, we study the boundedness of the solutions of some Volterra difference equations.

• 대한수학회지
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• 제43권3호
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• pp.635-658
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• 2006

This paper is concerned with giving some rather weak size conditions implying the $L^P$ boundedness of the multiple Marcin-kiewicz integrals for some fixed $1\;<\;p\;<\;{\infty}$, which essentially improve and extend some known results.

• Journal of applied mathematics & informatics
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• 제26권1_2호
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• pp.375-381
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• 2008

Boundedness for the set of all the $\epsilon$-approximate solutions for convex optimization problems are considered. We give necessary and sufficient conditions for the sets of all the $\epsilon$-approximate solutions of a convex optimization problem involving finitely many convex functions and a convex semidefinite problem involving a linear matrix inequality to be bounded. Furthermore, we give examples illustrating our results for the boundedness.

• Journal of applied mathematics & informatics
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• 제31권3_4호
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• pp.513-522
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• 2013

This paper mainly deals with the stochastic control system, the existence and uniqueness of solutions and the behavior of solutions are investigated. Firstly, we obtain sufficient conditions which guarantee the existence and uniqueness of solutions to the stochastic control system. And then, boundedness of the solution to the system is achieved under mean-square linear growth condition.

• 대한수학회보
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• 제46권3호
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• pp.535-543
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• 2009

In this paper we study some properties of the Helton class of an operator. In particular, we show that the Helton class preserves the quasinilpotent property and Dunford's boundedness condition (B). As corollaries, we get that the Helton class of some quadratically hyponormal operators or decomposable subnormal operators satisfies Dunford's boundedness condition (B).