• 호남수학학술지
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• 제26권1호
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• pp.77-83
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• 2004

A class of topological algebras, which we call it a fundamental one, has already been introduced generalizing the famous Cohen factorization theorem to more general topological algebras. To prove the generalized versions of Cohen's theorem to locally multilplicatively convex algebras, and finally to fundamental topological algebras, the completness of the background spaces is one of the main conditions. The local convexity of the completion of a locally convex space is a well known fact and here we have a discussion on the completness of fundamental metrizable topological vector spaces.

• 대한수학회보
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• 제38권1호
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• pp.71-79
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• 2001

The purpose of this paper is to prove new equilibrium existence theorems of social systems with coordination under general conditions on the preference correspondence in locally convex spaces, and we also give an example which the previous existence results on SSC do not work but our theorem can be applied.

• 대한수학회지
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• 제41권1호
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• pp.131-143
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• 2004

Let Ε and F be locally convex spaces over C. We assume that Ε is a nuclear space and F is a Banach space. Let f be a holomorphic mapping from Ε into F. Then we show that f is of uniformly bounded type if and only if, for an arbitrary locally convex space G containing Ε as a closed subspace, f can be extended to a holomorphic mapping from G into F.

• Kyungpook Mathematical Journal
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• 제26권2호
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• pp.187-215
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• 1986

• 대한수학회보
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• 제27권2호
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• pp.189-196
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• 1990

In this paper, we try to generalize ultraproducts in the category of locally convex spaces. To do so, we introduce D-ultracolimits. It is known [7] that the topology on a non-trivial ultraproduct in the category T $V^{ec}$ of topological vector spaces and continuous linear maps is trivial. To generalize the category Ba $n_{1}$ of Banach spaces and linear contractions, we introduce the category L $C_{1}$ of vector spaces endowed with families of semi-norms closed underfinite joints and linear contractions (see Definition 1.1) and its subcategory, L $C_{2}$ determined by Hausdorff objects of L $C_{1}$. It is shown that L $C_{1}$ contains the category LC of locally convex spaces and continuous linear maps as a coreflective subcategory and that L $C_{2}$ contains the category Nor $m_{1}$ of normed linear spaces and linear contractions as a coreflective subcategory. Thus L $C_{1}$ is a suitable category for the study of locally convex spaces. In L $C_{2}$, we introduce $l_{\infty}$(I. $E_{i}$ ) for a family ( $E_{i}$ )$_{i.mem.I}$ of objects in L $C_{2}$ and then for an ultrafilter u on I. we have a closed subspace $N_{u}$ . Using this, we construct ultraproducts in L $C_{2}$. Using the relationship between Nor $m_{1}$ and L $C_{2}$ and that between Nor $m_{1}$ and Ba $n_{1}$, we show thatour ultraproducts in Nor $m_{1}$ and Ba $n_{1}$ are exactly those in the literatures. For the terminology, we refer to [6] for the category theory and to [8] for ultraproducts in Ba $n_{1}$..

• East Asian mathematical journal
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• 제6권1호
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• pp.111-121
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• 1990

Let E be a locally convex Hausdorff space and let $\Gamma$ be a calibration for E. In this note we proved that if E is sequentially complete and a multi-vaiued operaturA in E is $\Gamma$-accretive such that $D(A){\subset}Re$ (I+$\lambda$A) for all sufficiently small positive $\lambda$, then A generates a nonlinear $\Gamma$-contraction semiproup {T(t) ; t>0}. We also proved that if E is complete, $Gamma$ is a dually uniformly convex calibration, and an operator A is m-$\Gamma$-accretive, then the initial value problem $$\{{\frac{d}{dt}u(t)+Au(t)\;\ni\;0,\;t >0,\atop u(0)=x}\.$$ has a solution $u:[0,\infty){\rightarrow}E$ given by $u(t)=T(t)x={lim}\limit_{n\rightarrow\infty}(I+\frac{t}{n}A)^{-n}x$ each $x{\varepsilon}D(A)$.

• 대한수학회지
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• 제33권3호
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• pp.587-599
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• 1996

We assume throughout the paper that f(z) is a conformal function in the ipen unit disk $D = {z : $\mid$z$\mid$ < 1}$. In the rest of paper, conformal means analytic and locally univalent.

• 대한수학회보
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• 제38권1호
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• pp.113-120
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• 2001

Using the notions of admissibility, local convexity and measure of noncompactness, we give new fixed point theorems for quasicompact or condensing multivalued mappings with domains that are not necessarily convex subsets of an arbitrary topological vector space.

• 충청수학회지
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• 제14권1호
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• pp.105-111
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• 2001

The purpose of this paper is to give a new generalization of the well-known common fixed point theorem due to Markov-Kakutani in general settings.

• 한국경영과학회지
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• 제20권2호
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• pp.125-137
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• 1995

This paper provides a locally convergent algorithm and a globally convergent algorithm for a variational inequality problem over convex polyhedral. The algorithm are based on the B (ouligand)-differentiability of the solution of a nonsmooth equation derived from the variational in-equality problem. Convergences of the algorithms are achieved by the results of Pang[3].