• Journal of applied mathematics & informatics
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• 제28권1_2호
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• pp.487-498
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• 2010

For some $\phi$-sequences $\phi_1$, $\phi_2$ and $\phi_3$, and $\kappa$-function $\kappa_1$, $\kappa_2$ and $\kappa_3$ with $\kappa_1^{-1}(x)\kappa_2^{-1}(x)\;{\geq}\;\kappa_3^{-1}(x)$ for $x\;{\geq}\;0$, the Luxemburg norm is lower semi-continuous on ${\kappa}{\phi}BV_0$, and some specialized equivalent conditions are considered.

• Journal of applied mathematics & informatics
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• 제13권1_2호
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• pp.447-455
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• 2003

For some sequnces of monotone nondecreasing convex $\Phi$-functions $\Phi$$_1$, $\Phi$$_2$ and $\Phi$$_3$and $textsc{k}$-functions $textsc{k}$$_1$, $textsc{k}$$_2$ and $textsc{k}$$_3$, we obtain the most general Holder type inequalities, and some special cases are considered for the functions of $textsc{k}$G$\Phi$-bounded variations.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.291-299
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• 2009

For $G_{\phi}$-sequences ${\phi}_i$ and ${\kappa}$-functions ${\kappa}_i$(i = 1,2,3) we obtain the most general $H{\ddot{o}}lder$ type inequalities on the functions of $G_{\kappa}G_{\phi}$-bounded variations.

• Korean Journal of Mathematics
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• 제12권2호
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• pp.117-125
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• 2004

We investigate some properties of functions of ${\Phi}{\Lambda}$-bound variation on a closed bounded interval, which is the generalization of bounded variation.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.545-553
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• 1997

By using the decreasing rearrangement of nonoverlapping subintervals of a closed bounded intervals and L.C.young's series for two ø-sequences we obtain some results concerning Riemann-Stieltijes integrals of functions of $\textsc{k}{\phi}-bounded$ variations.

• 대한수학회지
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• 제34권3호
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• pp.581-598
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• 1997

This paper is concerned with the impulsive control problem $$ \dot{x}(t) = f(t, x) + g(t, x)\dot{u}(t), t \in [0, T], x(0) = \overline{x}, $$ where u is a possibly discontinuous control function of bounded variation, $f : R \times R^n \mapsto R^n$ is a bounded and Lipschitz continuous function, and $g : R \times R^n \mapsto R^n$ is continuously differentiable w.r.t. the variable x and satisfies $\mid$g(t,\cdot) - g(s,\cdot)$\mid$ \leq \phi(t) - \phi(s)$, for some increasing function $\phi$ and every s < t. We show that the map $u \mapsto x_u$ is Lipschitz continuous when u ranges in the set of step functions whose total variations are uniformly bounded, where $x_u$ is the solution of the impulsive control system corresponding to u. We also define the generalized solution of the impulsive control system corresponding to a measurable control functin of bounded variation.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1995년도 추계학술대회 학술발표 논문집
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• pp.314-321
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• 1995

This paper discuss some properties of non-monotonic fuzzy measures of Ф -bounded variation. We show that there is an example of Ф such that $\beta$V(x, F) is a proper subspace of Ф$\beta$V(x, F) And also, we prove that Ф$\beta$V(x, F) is a real Banach space. Furthermore, we investigate some properties of non-monotonic fuzzy Ф -measures.

• 한국수학사학회지
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• 제19권2호
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• pp.115-124
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• 2006

유계변동(bounded variation)과 관련된 Daniel Waterman의 30여 년간의 연구에 대하여 조사를 하였다.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.557-562
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• 2006

We consider the relationship between absolute continuity for functions of a real variable and absolute continuity of functions of generalized bounded variation. Here, we obtain necessary and sufficient conditions between these two functions.

• 대한수학회보
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• 제23권2호
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• pp.171-175
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• 1986