• Nonlinear Functional Analysis and Applications
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• 제26권1호
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• pp.165-175
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• 2021

In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumbán, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrović-Hussain-Sen-Radenović on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권1호
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• pp.9-14
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• 2001

In some problems of abstract approximation theory the approximating set depends on some parameter p. In this paper, we make a set M(f) depends on the element f, $\phi$ and then best approximations are sought from a subset M(f) of M.

• Journal of Applied and Pure Mathematics
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• 제4권3_4호
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• pp.185-209
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• 2022

Here we exhibit multivariate quantitative approximations of Banach space valued continuous multivariate functions on a box or ℝ^N, N ∈ ℕ, by the multivariate normalized, quasi-interpolation, Kantorovich type and quadrature type neural network operators. We treat also the case of approximation by iterated operators of the last four types. These approximations are achieved by establishing multidimensional Jackson type inequalities involving the multivariate modulus of continuity of the engaged function or its high order Fréchet derivatives. Our multivariate operators are defined by using a multidimensional density function induced by the generalized symmetrical sigmoid function. The approximations are point-wise and uniform. The related feed-forward neural network is with one hidden layer.

• ETRI Journal
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• 제16권4호
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• pp.27-47
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• 1995

This paper improves top-down execution models of logic programs based on a two-phase abstract interpretation which consists of a bottom-up analysis followed by a top-down one. The two-phase analysis provides an approximation of all (possibly non-ground) success patterns of clauses relevant to a query. It is specialized by considering Sato and Tamaki’s depth k abstraction as abstract function. By the ability of the analysis to approximate possibly non-ground success patterns of clauses relevant to a query, it can be statically determined whether some subgoals will fail during execution and some succeeding subgoals do not participate in success patterns of program clauses relevant to a given query. These properties are utilized to improve execution models. This approach can be easily applied to any top-down (parallel) execution models. As instances, it is shown to be applicable to linear execution model and AND/OR Process Model.

• 한국공간정보시스템학회 논문지
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• 제7권2호
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• pp.57-66
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• 2005

고속도로 연결문제(Interconnecting Highways problem)는 VLSI 설계, 광 또는 유선 네트워크의 설계, 도로 건설 계획 등의 분야에서 도출되는 여러 가지 배치문제들을 대표하는 추상화 된 문제이다. 도로 건설에 있어 기존의 지점들을 가장 짧은 거리로 상호 연결하는 도로망은 다른 도로망들에 비해 경제적인 면에서 많은 이익을 가져다준다. 즉, 기존의 도로나 도시들을 상호 연결하는 새로운 도로망을 찾는 문제는 중요한 이슈가 된다. 본 논문에서는 NP-hard 문제인 고속도로 연결문제에 대해 '최적에 점근하는 결과치'를 내는 근사방법을 제안한다. 이 방법은 컴퓨팅 자원이 지원되는 한 최적치에 점근하는 근사-결과치를 구할 수 있도록 한다. 따라서 실제 응용에서는 제안된 근사방법에서 산출되는 근사치를 사실상의 최적치로 간주할 수 있게 된다. 선행연구에서의 근사방법과 달리 본 논문에서 제안된 방법은 주어진 문제 인스턴스의 속성에 부합하는 알고리즘을 만들어 낼 수 있도록 하는 큰 장점을 가진다.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.699-721
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• 2015

This paper investigates the existence of mild solution for a fractional integro-differential equations with a deviating argument and nonlocal initial condition in an arbitrary separable Hilbert space H via technique of approximations. We obtain an associated integral equation and then consider a sequence of approximate integral equations obtained by the projection of considered associated nonlocal fractional integral equation onto finite dimensional space. The existence and uniqueness of solutions to each approximate integral equation is obtained by virtue of the analytic semigroup theory via Banach fixed point theorem. Next we demonstrate the convergence of the solutions of the approximate integral equations to the solution of the associated integral equation. We consider the Faedo-Galerkin approximation of the solution and demonstrate some convergenceresults. An example is also given to illustrate the abstract theory.

• 대한전자공학회논문지TC
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• 제44권8호
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• pp.62-67
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• 2007

센서네트워크 중에는 센서노드들이 넓은 지역에 걸쳐 정해진 위치에 산재되어야 하는 경우가 있다. 이런 경우 센서노드들을 interconnect하기 위한 최소개수의 연결노드들을 추가하는 문제가 대두되며, 이는 The Minimum number of Steiner Points라는 추상화된 문제로 귀결된다. 이 문제는 NP-hard 문제이므로, 본 논문에서는 문제가 내포하는 기하학적인 성질을 이용하여 연결노드의 최소개수에 근접하는 방안을 제시한다. 센서네트워크에서 노드의 개수를 줄임으로써 네트워크 내부에서 오가는 메시지의 교환량이 대폭 감소하게 된다.

• Kyungpook Mathematical Journal
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• 제56권1호
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• pp.221-233
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• 2016

The present paper proposes a new monotone iteration method for existence as well as approximation of the coupled solutions for a coupled periodic boundary value problem of first order ordinary nonlinear differential equations. A new hybrid coupled fixed point theorem involving the Dhage iteration principle is proved in a partially ordered normed linear space and applied to the coupled periodic boundary value problems for proving the main existence and approximation results of this paper. An algorithm for the coupled solutions is developed and it is shown that the sequences of successive approximations defined in a certain way converge monotonically to the coupled solutions of the related differential equations under some suitable mixed hybrid conditions. A numerical example is also indicated to illustrate the abstract theory developed in the paper.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제11권4호
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• pp.1-8
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• 2007

In some wireless sensor networks, the sensor nodes are required to be located sparsely at designated positions over a wide area, introducing the problem of adding minimum number of relay nodes to interconnect the sensor nodes. The problem finds its a bstract form in literature: the Minimum number of Steiner Points. Since it is known to be NP-hard, this paper proposes an approximation scheme to estimate the minimum number of relay nodes through the properties of the abstract form. Note that by reducing the numb er of nodes in a sensor network, the amount of data exchange over the net will be far decreased.

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.433-446
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• 1997

In this paper we study an existence and the approxi-mation of the solution of the solution of the elliptic variational inequality from an abstract axiomatic point of view. We discuss convergence results and give an error estimate for the difference of the two solutions in an appropriate norm Also we present some computational results by using fixed point method.