• Communications of the Korean Mathematical Society
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• v.10 no.3
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• pp.699-705
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• 1995

We first generalize the Volodin space which Volodin constructed in order to define a new algebraic K-theory. We investigate the topological (homotopy) properties of the general Volodin space. We also provide a theorem which seems to be useful in pure homotopy theory. We prove that $V(*_\alpha G_\alpha, {G_\alpha})$ is simply connected.

• Communications of the Korean Mathematical Society
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• v.12 no.4
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• pp.975-984
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• 1997

In the Finsler space with an $(\alpha, \beta)$-metric, we can consider the difference tensors of the Finsler connection. The properties of the conformal transformation of these difference tensors are investigated in the present paper. Some conformal invariant tensors are formed in the Finsler space with an $(\alpha, \beta)$-metric related with the difference tensors.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.1035-1046
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• 2015

In this work we present some geometric properties (like star-likeness and convexity of order ${\alpha}$ and also close-to-convexity of order ($1+{\alpha}$)/2) for normalized of Lommel functions of the first kind. In order to prove our main results, we use the technique of differential subordinations and some inequalities. Furthermore, we present some applications of convexity involving Lommel functions associated with the Hardy space of analytic functions, i.e., we obtain conditions for the function $h_{{\mu},{\upsilon}}(z)$ to belong to the Hardy space $H^p$.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.447-452
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• 2008

We provide some examples around AP and WAP spaces which are connected with higher convergence properties-radiality, semiradiality and pseudoradiality. We also prove a theorem (Theorem 3.2) that (a) any pseudo-open continuous image of an AP-space is an AP-space and (b) any pseudo-open continuous image of an WAP-space is an WAP-space. This answers the question posed by V. V. Tkachuk and I. V. Yaschenko [10].

• Korean Journal of Mathematics
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• v.6 no.1
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• pp.47-66
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• 1998

In this paper, we introduce an $L_p$ analytic Fourier-Feynman transformation, show the existence of the $L_p$ analytic Fourier-Feynman transforms for a certain class of cylinder functionals on an abstract Wiener space, and investigate its interesting properties. Moreover, we define a convolution product for two functionals on the abstract Wiener space and establish the relationships between the Fourier-Feynman transform for the convolution product of two cylinder functionals and the Fourier-Feynman transform for each functional.

• Bulletin of the Korean Mathematical Society
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• v.44 no.2
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• pp.291-308
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• 2007

The motivation of this paper is to present a new and interesting notion of intuitionistic fuzzy n-normed linear space. Cauchy sequence and convergent sequence in intuitionistic fuzzy n-normed linear space are introduced and we provide some results onit. Furthermore we introduce generalized cartesian product of the intuitionistic fuzzy n-normed linear space and establish some of its properties.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.359-365
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• 1998

We give two sufficient conditions that the space (X,C*) be a Fr$\acute{e}$chet-Urysohn space such that $x_n \to x$ in (X,c) if and only if $x_n \to x$ in (X,c*), where c* is the sequential closure operator on a generalized topological (X,c).

• Communications of the Korean Mathematical Society
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• v.14 no.2
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• pp.329-336
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• 1999

We construct the Gelfand triple based on the space \ulcorner, introduced by Sato and di Silva, of analytic and exponentially decreasing function. This space denoted by(\ulcorner) of white noise test functionals are defined by the operator cosh \ulcorner, A=-(\ulcorner)\ulcorner+x\ulcorner+1. We also note that many properties like generalizations of the Paley-Wiener theorem and the Bochner-Schwartz theorem hold in this space as in the space of Hida distributions.

• Journal of the Korean Mathematical Society
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• v.48 no.5
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• pp.1043-1052
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• 2011

We introduce a new norm, called the $N^p$-norm (1 $\leq$ p < ${\infty}$ on the space $N^p$(V,W) where V and W are abstract operator spaces. By proving some fundamental properties of the space $N^p$(V,W), we also discover that if W is complete, then the space $N^p$(V,W) is also a Banach space with respect to this norm for 1 $\leq$ p < ${\infty}$.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.11a
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• pp.252-255
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• 1997

In this paper, we will propose the methodology of data analysis using the fuzzy property set model. In real world, the data can be represented with the object. $\theta$. and the property, $\pi$, and its has-property relation, P. Then, the conceptual space can be defined with the chosen properties. Each object has a unique location in the conceptual space. In Fuzzy mode, the fuzzy property, and fuzzy conceptual space can be redefined. To analyze data using the fuzzy property set model, the rough set need to be defined in the fuzzy conceptual space.