• 한국수학교육학회지시리즈A:수학교육
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• 제25권3호
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• pp.43-45
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• 1987

In this paper we will investigate the relations between Dunford-Pettis operators and weakly compact operators. And we get a characterization of a Banach space with the RNP.

• 대한수학회보
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• 제20권2호
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• pp.87-93
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• 1983

Let X and Y be normed linear spaces. An operator T defined on X with the range in Y is continuous in the sense that if a sequence {x$_{n}$} in X converges to x for the weak topology .sigma.(X.X') then {Tx$_{n}$} converges to Tx for the norm topology in Y. We shall denote the class of such operators by WC(X, Y). For example, if T is a compact operator then T.mem.WC(X, Y). In this note we discuss relationships between WC(X, Y) and the class of weakly of bounded linear operators B(X, Y). In the last section, we will consider some characters for an operator in WC(X, Y).).

• 대한수학회논문집
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• 제28권4호
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• pp.669-677
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• 2013

In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if N is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if N is a NI near-ring, then for every $a{\in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){\setminus}int\;V(a)$.

• 충청수학회지
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• 제34권4호
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• pp.369-378
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• 2021

In this paper, we give an upper bound for the fundamental tone of stable constant mean curvature hypersurfaces in hyperbolic space. Let M be an n-dimensional complete non-compact constant mean curvature hypersurface with finite L²-norm of the traceless second fundamental form. If M is weakly stable, then λ₁(M) is bounded above by n² + O(n^2+s) for arbitrary s > 0.

• 대한수학회지
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• 제44권2호
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• pp.261-273
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• 2007

In this paper, we introduce some new properties of a topological space which are respectively generalizations of $Fr\'{e}chet$-Urysohn property. We show that countably AP property is a sufficient condition for a space being countable tightness, sequential, weakly first countable and symmetrizable, to be ACP, $Fr\'{e}chet-Urysohn$, first countable and semimetrizable, respectively. We also prove that countable compactness is a sufficient condition for a countably AP space to be countably $Fr\'{e}chet-Urysohn$. We then show that a countably compact space satisfying one of the properties mentioned here is sequentially compact. And we show that a countably compact and countably AP space is maximal countably compact if and only if it is $Fr\'{e}chet-Urysohn$. We finally obtain a sufficient condition for the ACP closure operator $[{\cdot}]_{ACP}$ to be a Kuratowski topological closure operator and related results.

• 대한수학회보
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• 제31권2호
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• pp.289-295
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• 1994

Let (A,G,.alpha.) be a $C^{*}$-dynamical system. In [3] the classical notions of ergodic properties of topological dynamical systems such as topological transitivity, minimality, and uniquely ergodicity are extended and analyzed in the context of non-abelian $C^{*}$-dynamical systems. We showed in [2] that if G is a compact group, then minimality, topological transitivity, uniquely ergodicity, and weakly ergodicity of the $C^{*}$-dynamical system (A,G,.alpha.) are equivalent.alent.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제6권1호
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• pp.70-76
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• 2006

Some Stampacchia type of generalized weak vector quasivariational-like inequalities for fuzzy mappings was introduced and the existence of solutions to them under non-compact assumption was considered using the particular form of the generalized Ky Fan's section theorem due to Park [15]. As a corollary, Stampacchia type of generalized vector quasivariational-like inequalities for fuzzy mappings was studied under compact assumption using Ky Fan's section theorem [7].

• 호남수학학술지
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• 제27권2호
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• pp.251-265
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• 2005

In this paper, we introduce a generalized vector quasivariational like inequality for fuzzy mappings and show the existence of solutions under compact assumption.

• 대한수학회보
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• 제39권4호
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• pp.665-669
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• 2002

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권1호
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• pp.1-5
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• 2018

It is proved that 'maximum' is actually attained in the following risk measure representation $${\rho}_m(X)={max \atop Q{\in}Q_m}E_Q[-X]$$.