• Title/Summary/Keyword: Bounded variation

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DIRICHLET-JORDAN THEOREM ON $SIM$ SPACE

  • Kim, Hwa-Joon;Lekcharoen, S.;Supratid, S.
    • Korean Journal of Mathematics
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    • v.17 no.1
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    • pp.37-41
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    • 2009
  • We would like to propose Dirichlet-Jordan theorem on the space of summable in measure(SIM). Surely, this is a kind of extension of bounded variation([1, 4]), and considered as an application of fuzzy set such that ${\alpha}$-cut is 0.

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ABSOLUTE CONTINUITY OF FUNCTIONS OF ${\phi}{\Lambda}BV$

  • Kim Hwa-Jun
    • Journal of applied mathematics & informatics
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    • v.22 no.1_2
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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.

ON DENJOY*-STIELTJES INTEGRAL

  • Oh, Mee Na;Park, Chun-Kee
    • Korean Journal of Mathematics
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    • v.16 no.4
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    • pp.499-509
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    • 2008
  • In this paper we introduce the concepts of the generalized bounded variation in the restricted sense with respect to a strictly increasing function and $Denjoy_*$-Stieltjes integral of real-valued functions and investigate their properties.

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Efficient Multicast Tree Algorithm for Acceptable Delay and Minimum Delay Variation (지연시간 한계의 만족과 효율적인 최소 지연변이 멀티캐스트 트리 생성 알고리즘)

  • Kim Moon-Seong;Choo Hyun-Seung;Lee Young-Ro
    • The KIPS Transactions:PartC
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    • v.12C no.1 s.97
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    • pp.105-110
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    • 2005
  • With the proliferation of multimedia group applications, the construction of multicast trees satisfying QoS requirements is becoming a problem of prime importance. In this paper, we study the delay- and delay variation-bounded multicast tree (DVBMT) problem which is NP-complete. The problem is to construct a spanning tree for destination node, which has the minimized multicast delay variation, and the delay on the path from the source to each destination is bounded. A solution to this problem is required to provide decent real-time communication services such as on-line games, shopping, and teleconferencing. Performance comparison shows that the proposed scheme outperforms DDVCA which is known to be effective so far in any network topology. The enhancement is up to about $3.6{\%}{\~}11.1{\%}$ in terms of normalized surcharge for DUVCA. The time complexity of our algorithm is $O(mn^2)$.

SEQUENCES IN THE RANGE OF A VECTOR MEASURE

  • Song, Hi Ja
    • Korean Journal of Mathematics
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    • v.15 no.1
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    • pp.13-26
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    • 2007
  • We prove that every strong null sequence in a Banach space X lies inside the range of a vector measure of bounded variation if and only if the condition $\mathcal{N}_1(X,{\ell}_1)={\Pi}_1(X,{\ell}_1)$ holds. We also prove that for $1{\leq}p<{\infty}$ every strong ${\ell}_p$ sequence in a Banach space X lies inside the range of an X-valued measure of bounded variation if and only if the identity operator of the dual Banach space $X^*$ is ($p^{\prime}$,1)-summing, where $p^{\prime}$ is the conjugate exponent of $p$. Finally we prove that a Banach space X has the property that any sequence lying in the range of an X-valued measure actually lies in the range of a vector measure of bounded variation if and only if the condition ${\Pi}_1(X,{\ell}_1)={\Pi}_2(X,{\ell}_1)$ holds.

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The Algorithm of Efficient Core Selection Estimation for the Multicast Delay Variation Problem and Minimum Delay Variation (멀티캐스트 지연변이 문제에 대한 효율적인 코어 선택 추정 알고리즘)

  • Ahn, Youn-Gjin;Kim, Moon-Seong;Choo, Hyun-Seung
    • Journal of Internet Computing and Services
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    • v.8 no.2
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    • pp.33-41
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    • 2007
  • With the development of the multicast technology, the realtime strategy among the group applications using the multicast routing is getting more important. An essential factor of these real-time application is to optimize the Delay- and delay Variation-Bounded Multicast Tree(DVBMT) problem. This problem is to satisfy the minimum delay variation and the end-to-end delay within an upper bound. The DVBMT problem is known as NP-complete problem. The representative algorithms for the problem are DVMA, DDVCA, and so on. In this paper, we show that the proposed algorithm outperforms any other algorithm. The efficiency of our algorithm is verified through the prerformance evaluation and the enhancement is up to about 9% to 29% in terms of the multicast delay variation. The time complexity of our algorithm is $O(mn^2)$M.

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ON THE OSTROWSKI INEQUALITY FOR THE RIEMANN-STIELTJES INTEGRAL ${\int}_a^b$ f (t) du (t), WHERE f IS OF HÖLDER TYPE AND u IS OF BOUNDED VARIATION AND APPLICATIONS

  • DRAGOMIR, S.S.
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.5 no.1
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    • pp.35-45
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    • 2001
  • In this paper we point out an Ostrowski type inequality for the Riemann-Stieltjes integral ${\int}_a^b$ f (t) du (t), where f is of p-H-$H{\ddot{o}}lder$ type on [a,b], and u is of bounded variation on [a,b]. Applications for the approximation problem of the Riemann-Stieltjes integral in terms of Riemann-Stieltjes sums are also given.

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Szász-Kantorovich Type Operators Based on Charlier Polynomials

  • Kajla, Arun;Agrawal, Purshottam Narain
    • Kyungpook Mathematical Journal
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    • v.56 no.3
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    • pp.877-897
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    • 2016
  • In the present article, we study some approximation properties of the Kantorovich type generalization of $Sz{\acute{a}}sz$ type operators involving Charlier polynomials introduced by S. Varma and F. Taşdelen (Math. Comput. Modelling, 56 (5-6) (2012) 108-112). First, we establish approximation in a Lipschitz type space, weighted approximation theorems and A-statistical convergence properties for these operators. Then, we obtain the rate of approximation of functions having derivatives of bounded variation.