• Korean Journal of Mathematics
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• 제28권4호
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• pp.915-929
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• 2020

We prove a fixed point theorem for generalized asymptotic pointwise nonexpansive mapping in the setting of a hyperbolic space. A one-step iterative scheme approximating common fixed point of two generalized asymptotic pointwise (quasi-) nonexpansive mappings in this setting is provided. We obtain ∆-convergence and strong convergence theorems of the iterative scheme for two generalized asymptotic pointwise nonexpansive mappings in the same setting. Our results generalize and extend some related results in the literature.

• Korean Journal of Mathematics
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• 제26권3호
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• pp.483-501
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• 2018

In this paper, we present some recent results on weighted pointwise convergence and the rate of pointwise convergence for the family of nonlinear double singular integral operators in the following form: $$T_{\eta}(f;x,y)={\int}{\int\limits_{{\mathbb{R}^2}}}K_{\eta}(t-x,\;s-y,\;f(t,s))dsdt,\;(x,y){\in}{\mathbb{R}^2},\;{\eta}{\in}{\Lambda}$$, where the function $f:{\mathbb{R}}^2{\rightarrow}{\mathbb{R}}$ is Lebesgue measurable on ${\mathbb{R}}^2$ and ${\Lambda}$ is a non-empty set of indices. Further, we provide an example to support these theoretical results.

• 한국통신학회논문지
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• 제16권11호
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• pp.1194-1200
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• 1991

유한요소법(Finite Element Method)은 컴퓨터를 이용하여 미분방정식의 근사해를 얻기위한 수학적인 기법이다. 유한요소법의 pointwise convergence는 매쉬 크기와 허용 오차와의 관계를 분석해 보려는 것이다. 이들 상호 관계에 과난 연구는 유한요소법에 의한 근사식의 질을 높이는데 중요한 계기가 되어 결과를 예측 하는데 효과적이다. 본 논문을 1-Irregular 매쉬를 이용한 세분화(refinement) 및 형상 함수의 차수 변화에 따른 미지절점(unknown node) 수의 증가에 따른 수렴성을 분석하였다.

• 한국수학교육학회지시리즈A:수학교육
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• 제31권2호
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• pp.121-132
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• 1992

FEM(Finite Element Method)의 pointwise convergence는 mesh size와 허용오차와의 관계를 분석해 보려는 것이다. 이들 상호 관계에 관한 연구는 FEM에 의한 근사식의 질을 높이는데 중요한 계기가 되어 결과 예측을 하는데 효과적이다. 본 논문은 1-irregular mesh를 이용한 세분화(refinement)로 미지점(unknon node)dlm 수를 최소화 하면서 원하는 점에서의 수렴성을 비교 분석하였다.

• 대한수학회논문집
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• 제31권3호
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• pp.575-583
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• 2016

In this paper, we study the modified S-iteration process for asymptotic pointwise nonexpansive mappings in a uniformly convex hyperbolic metric space. We then prove the convergence of the sequence generated by the modified S-iteration process.

• 대한수학회보
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• 제36권4호
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• pp.717-722
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• 1999

The set of continuous maps of a space X to real usual space R equipped with the toplogy of pointwise convergence will be denoted by $C_p$(X). In this paper, we prove that; $C_p$(X) is hereditarily separable and hereditary Lindelof if and only if $X^n$ is hereditarily separable and hereditary Lindelof.

• 대한수학회보
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• 제38권1호
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• pp.81-91
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• 2001

The expansion of a distribution of $K^r_M^r(R)$ in terms of regular orthogonal wavelets is considered. The expansion of a distribution of $K^r_M^r(R)$ is shown to converge pointwise to the value of the distribution where is exists.

• 대한수학회논문집
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• 제12권1호
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• pp.127-133
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• 1997

In order to study the limits of sequences appearing in, for example, stochastic process, A. V. Skorokhod has defined new function space topologies. We compare these topologies with the topology of compact convergence, the topology of pointwise convergence and others.

• Korean Journal of Mathematics
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• 제25권4호
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• pp.483-494
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• 2017

In the current manuscript, we investigate the pointwise convergence of the singular integral operators involving power nonlinearity given in the following form: $$T_{\lambda}(f;x)={\int_a^b}{\sum^n_{m=1}}f^m(t)K_{{\lambda},m}(x,t)dt,\;{\lambda}{\in}{\Lambda},\;x{\in}(a,b)$$, where ${\Lambda}$ is an index set consisting of the non-negative real numbers, and $n{\geq}1$ is a finite natural number, at ${\mu}$-generalized Lebesgue points of integrable function $f{\in}L_1(a,b)$. Here, $f^m$ denotes m-th power of the function f and (a, b) stands for arbitrary bounded interval in ${\mathbb{R}}$ or ${\mathbb{R}}$ itself. We also handled the indicated problem under the assumption $f{\in}L_1({\mathbb{R}})$.

• Korean Journal of Mathematics
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• 제7권1호
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• pp.45-51
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• 1999

Let X and Y be topological vector spaces. For a sequence {$T_j$} of bounded operators from X into Y the $c_0$-multiplier convergence of ${\sum}T_j$ is an invariant on topologies which are stronger (need not strictly) than the topology of pointwise convergence on X but are weaker (need not strictly) than the topology of uniform convergence on bounded subsets of X.