• Journal of Applied and Pure Mathematics
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• 제4권1_2호
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• pp.37-50
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• 2022

In this article we define and study the notions of $\mathcal{I}$-convergence and $\mathcal{I}$-Cauchy of triple sequences in the topology induced by random 2-normed spaces and prove some theorems based on them.

• East Asian mathematical journal
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• 제26권2호
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• pp.179-190
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• 2010

We study the theoretical background on the relationship between the equality property and operations treated in different sub-areas in secondary school mathematics curriculum respectively studied. Furthermore, we discuss in detail the equality property in rational numbers field $\mathbb{Q}$ and the real numbers field $\mathbb{R}$. Through this study, professional knowledges of school teachers are enhanced so that these aforementioned knowledges are connected smoothly to teaching activities in classrooms.

• 충청수학회지
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• 제21권3호
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• pp.347-354
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• 2008

In this paper, we will show that ($CF(X,K),{\chi}_{{\parallel}{\mid}{\cdot}{\parallel}{\mid}}$) is a fuzzy Banach space using that the dual space $X^*$ of a normed linear space X is a crisp Banach space. And for a normed linear space Y instead of a scalar field K, we obtain ($CF(X,Y),{\rho}^*$) is a fuzzy Banach space under the some conditions.

• 대한수학회지
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• 제52권6호
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• pp.1287-1303
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• 2015

The Hausdorff topology induced by a fuzzy metric space under more weak assumptions is investigated in this paper. Another purpose of this paper is to obtain the Banach contraction theorem in fuzzy metric space based on a natural concept of Cauchy sequence in fuzzy metric space.

• 대한수학회지
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• 제33권4호
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• pp.891-908
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• 1996

Let (X,d) be a metric space and let T be a mapping from X into itself. We say that a metric space (X,d) is T-orbitally complete if every Cauchy sequence of the form ${T^{n_i}x}_{i \in N}$ for $x \in X$ converges to a point in X.

• 대한수학회보
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• 제52권3호
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• pp.987-998
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• 2015

In the paper, the authors discover an integral representation, some inequalities, and complete monotonicity of the Bernoulli numbers of the second kind.

• 제어로봇시스템학회:학술대회논문집
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• 제어로봇시스템학회 1989년도 한국자동제어학술회의논문집; Seoul, Korea; 27-28 Oct. 1989
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• pp.1140-1145
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• 1989

A general dynamic iterative learning control scheme is proposed for a class of nonlinear systems. Relying on stabilizing high-gain feedback loop, it is possible to show the existence of Cauchy sequence of feedforward control input error with iteration numbers, which results in a uniform convergance of system state trajectory to the desired one.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제10권2호
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• pp.152-156
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• 2010

We define some terminologies on intuitionistic fuzzy metric space and prove that the topology generated by any intuitionistic fuzzy metric space is metrizable. Also, we show that if the intuitionistic fuzzy metric space is complete, then the generated topology is completely metrizable, a Baire space, and that an intuitionistic fuzzy metric space is precompact if and only if every sequence has a Cauchy subsequence.

• 대한수학회논문집
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• 제27권2호
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• pp.265-277
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• 2012

In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

• 한국지능시스템학회논문지
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• 제15권5호
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• pp.639-642
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• 2005

In this paper, we introduce the notions of the convergence in the sense of ${\alpha}$-level and the fuzzy completeness on a fuzzy normed linear space. And we investigate related properties.