• 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.

• 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.

• 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.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.571-577
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• 2005

The aim of this paper is to establish the rate of convergence of Baskakov-Durrmeyer operators for bounded variation function. We have given the better estimate over the results due to Guo ([4]), Anial and Teberska ([1]) and Gupta and Srivastava ([8]).

• 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 $O(mn^2)$.

• 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.

• 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.

• 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.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.8 no.1
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• pp.31-40
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• 2004

In this paper we point out an approximation for the Fourier transform for functions of bounded variation and study the approximation error of certain associated quadrature rules.

• 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.