• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.379-384
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• 2003

In this paper, we obtain a topology $\tau\delta$ on X. From this topology, we obtain some characterizations of if-closed spaces.

• Kyungpook Mathematical Journal
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• 제50권4호
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• pp.537-543
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• 2010

Let X be a regular $T_1$-space such that each single point set is a $G_{\delta}$ set. Denot 'hereditarily closure-preserving' by 'HCP'. To consider a question of closed maps of S. Lin in [6], we improve some results of Foged in [1], and prove the following propositions. Proposition 1. $D\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}:x{\in}F\}\mid{\geq}{\aleph}_0\}$ is discrete and closed if $\cal{F}$ is a collection of HCP. Proposition 2. $\cal{H}\;=\;\{{\cup}\cal{F}'\;:\;F'$ is an fininte subcolletion of $\cal{F}_n\}$ is HCP if $\cal{F}$ is a collection of HCP. Proposition 3. Let (X,$\tau$) have a $\sigma$-HCP k-network. Then (X,$\tau$) has a $\sigma$-HCP k-network F = ${\cup}_n\cal{F}_n$ such that such tat: (i) $\cal{F}_n\;\subset\;\cal{F}_{n+1}$, (ii) $D_n\;=\;\{x{\in}X\;:\;\mid\{F{\in}\cal{F}_n\;:\;x{\in}F\}\mid\;{\geq}\;{\aleph}_0\}$ is a discrete closed set and (iii) each $\cal{F}_n$ is closed to finite intersections.

• 호남수학학술지
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• 제39권4호
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• pp.575-590
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• 2017

A new class of functions called $R_{\theta}$-supercontinuous functions is introduced. Their basic properties are studied and their place in the hierarchy of strong variants of continuity, which already exist in the literature, is elaborated. The class of $R_{\theta}$-supercontinuous functions properly contains the class of $R_z$-supercontinuous functions [39] which in turn properly contains the class of $R_{cl}$-supercontinuous functions [43] and so includes all cl-supercontinuous (clopen continuous) functions ([38], [34]) and is properly contained in the class of $R_{\delta}$-supercontinuous functions [24].

• Communications for Statistical Applications and Methods
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• 제15권2호
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• pp.147-159
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• 2008

We consider using ranked set sampling methods to draw inference about the three well-known measures of overlap, namely Matusita's measure $\rho$, Morisita's measure $\lambda$ and Weitzman's measure $\Delta$. Two exponential populations with different means are considered. Due to the difficulties of calculating the precision or the bias of the resulting estimators of overlap measures, because there are no closed-form exact formulas for their variances and their exact sampling distributions, Monte Carlo evaluations are used. Confidence intervals for those measures are also constructed via the bootstrap method and Taylor series approximation.

• 대한수학회논문집
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• 제9권2호
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• pp.331-336
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• 1994

Let $P_{0}$ be a $\delta$-ring (a ring closed with respect to the forming of countable intersections) of subsets of a nonempty set $\Omega$. Let X and Y be Banach spaces and L(X, Y) the Banach space of all bounded linear operators from X to Y. A set function m : $P_{0}$ longrightarrow L(X, Y) is called an operator valued measure countably additive in the strong operator topology if for every x $\epsilon$ X the set function E longrightarrow m(E)x is a countably additive vector measure. From now on, m will denote an operator valued measure countably additive in the strong operator topology.(omitted)

• East Asian mathematical journal
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• 제24권1호
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• pp.35-43
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• 2008

Let E be a uniformly convex Banach space and K be a nonempty closed convex subset of E. Let ${\{T_i\}}^N_{i=1}$ be N nonexpansive self-mappings of K with $F\;=\;{\cap}^N_{i=1}F(T_i)\;{\neq}\;{\theta}$ (here $F(T_i)$ denotes the set of fixed points of $T_i$). Suppose that one of the mappings in ${\{T_i\}}^N_{i=1}$ is semi-compact. Let $\{{\alpha}_n\}\;{\subset}\;[{\delta},\;1-{\delta}]$ for some ${\delta}\;{\in}\;(0,\;1)$ and $\{{\beta}_n\}\;{\subset}\;[\tau,\;1]$ for some ${\tau}\;{\in}\;(0,\;1]$. For arbitrary $x_0\;{\in}\;K$, let the sequence {$x_n$} be defined iteratively by $\{{x_n\;=\;{\alpha}_nx_{n-1}\;+\;(1-{\alpha}_n)T_ny_n,\;\;\;\;\;\;\;\;\; \atop {y_n\;=\;{\beta}nx_{n-1}\;+\;(1-{\beta}_n)T_nx_n},\;{\forall}_n{\geq}1,}$, where $T_n\;=\;T_{n(modN)}$. Then {$x_n$} convergence strongly to a common fixed point of the mappings family ${\{T_i\}}^N_{i=1}$. The result presented in this paper generalized and improve the corresponding results of Chidume and Shahzad [C. E. Chidume, N. Shahzad, Strong convergence of an implicit iteration process for a finite family of nonexpansive mappings, Nonlinear Anal. 62(2005), 1149-1156] even in the case of ${\beta}_n\;{\equiv}\;1$ or N=1 are also new.

• 대한수학회논문집
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• 제35권1호
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• pp.301-319
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• 2020

In this paper, we show that the system of difference equations $x_n={\frac{ay^p_{n-1}+b(x_{n-2}y_{n-1})^{p-1}}{cy_{n-1}+dx^{p-1}_{n-2}}}$, $y_n={\frac{{\alpha}x^p_{n-1}+{\beta}(y_{n-2}x_{n-1})^{p-1}}{{\gamma}x_{n-1}+{\delta}y^{p-1}_{n-2}}}$, n ∈ ℕ₀ where the parameters a, b, c, d, α, β, γ, δ, p and the initial values x-2, x-1, y-2, y-1 are real numbers, can be solved. Also, by using obtained formulas, we study the asymptotic behaviour of well-defined solutions of aforementioned system and describe the forbidden set of the initial values. Our obtained results significantly extend and develop some recent results in the literature.

• 한국전자파학회논문지
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• 제22권10호
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• pp.1012-1015
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• 2011

눈 모형이 열린 경우 간결하고 좋은 수렴 특성을 갖는 결정-지향 자력 등화 알고리듬이 자주 사용된다. 그러나 눈 모형이 닫힌 채널에서 결정-지향 알고리듬의 수렴은 보장되지 않는다. 이러한 문제를 해결하기 위하여 무기억 비선형 함수로 hyperbolic tangent 함수를 사용하는 수정된 Bussgang 알고리듬의 적용이 Filho 등에 의하여 제안되었다. 그러나 이 알고리듬의 적용은 hyperbolic tangent 함수 그리고 이의 미분에 대한 계산 및 채널의 변화에 따른 룩업 테이블을 위한 많은 메모리를 필요로 한다. 따라서 본 논문에서는 Filho 등이 제안한 알고리듬의 계산량 또는 하드웨어 복잡도를 줄이기 위하여 결정-지향 알고리듬을 위한 개선된 기법을 제안한다. 무기억 비선형 함수를 signum 함수로 설정하고, 이의 미분인 디락 델타 함수(Dirac delta function)를 협소한 사각 펄스로 근사화하여 결정-지향 알고리듬에 적용하면 Filho가 제안한 알고리듬의 수렴 및 정상 상태 성능은 유지하면서 계산 복잡도를 크게 줄일 수 있다.