• Communications of the Korean Mathematical Society
• /
• v.14 no.1
• /
• pp.111-119
• /
• 1999

We consider the relations between locally convex spaces of generalized Sobolev spaces of Roumieu type.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.8 no.5
• /
• pp.1-4
• /
• 1998

The main goal of this paper is to investigate some properties of the locally convex fuzzy topological vector space.

• Korean Journal of Mathematics
• /
• v.5 no.2
• /
• pp.227-232
• /
• 1997

Banach-Steinhaus type results are established for sequentially continuous operators and bounded operators between locally convex spaces without barrelledness.

• Journal of the Korean Mathematical Society
• /
• v.40 no.2
• /
• pp.225-239
• /
• 2003

(G, <) is an ordered group if'<'is a total order relation on G in which f < g implies that xfy < xgy for all f, g, x, y $\in$ G. We say that (G, <) is centrally ordered if (G, <) is ordered and ［G,D］ $\subseteq$ C for every convex jump C $\prec$ D in G. Equivalently, if $f^{-1}g f{\leq} g^2$ for all f, g $\in$ G with g > 1. Every order on a torsion-free locally nilpotent group is central. We prove that if every order on every two-generator subgroup of a locally soluble orderable group G is central, then G is locally nilpotent. We also provide an example of a non-nilpotent two-generator metabelian orderable group in which all orders are central.

• Journal of the Chungcheong Mathematical Society
• /
• v.31 no.1
• /
• pp.177-182
• /
• 2018

The purpose of this paper is to present approximation of $C_0-sequentially$ equicontinuous semigroups on a sequentially complete locally convex space X.

• Journal of the Korean Mathematical Society
• /
• v.41 no.1
• /
• pp.51-64
• /
• 2004

Q-reflexive locally convex spaces are spaces where $\widehat{\bigotimes}_{n,s,\pi}\;{E_e}^{"}\;and\;\overline{{(P(^nE),\;\taub)_i}^'}$ are isomorphic in a canonical way for every n. We investigate properties and find examples of such spaces.

• Kyungpook Mathematical Journal
• /
• v.55 no.2
• /
• pp.473-484
• /
• 2015

Archimedes determined the center of gravity of a parabolic section as follows. For a parabolic section between a parabola and any chord AB on the parabola, let us denote by P the point on the parabola where the tangent is parallel to AB and by V the point where the line through P parallel to the axis of the parabola meets the chord AB. Then the center G of gravity of the section lies on PV called the axis of the parabolic section with $PG=\frac{3}{5}PV$. In this paper, we study strictly locally convex plane curves satisfying the above center of gravity properties. As a result, we prove that among strictly locally convex plane curves, those properties characterize parabolas.

• Journal of the Korean Mathematical Society
• /
• v.35 no.2
• /
• pp.491-502
• /
• 1998

We obtain new fixed point theorems on maps defined on "locally G-convex" subsets of a generalized convex spaces. Our first theorem is a Schauder-Tychonoff type generalization of the Brouwer fixed point theorem for a G-convex space, and the second main result is a fixed point theorem for the Kakutani maps. Our results extend many known generalizations of the Brouwer theorem, and are based on the Knaster-Kuratowski-Mazurkiewicz theorem. From these results, we deduce new results on collectively fixed points, intersection theorems for sets with convex sections and quasi-equilibrium theorems.

• Journal of the Chungcheong Mathematical Society
• /
• v.36 no.4
• /
• pp.279-288
• /
• 2023

We obtain a Chandrabhan type fixed point theorem for a multimap having a non-compact domain and a weakly closed graph, and taking convex values only on a quasi-convex subset of Hausdorff locally convex topological vector space. We introduce the definition of Chandrabhan-set and find a sufficient condition for every countably condensing multimap to have a relatively compact Chandrabhan-set. Finally, we establish a new version of Sadovskii fixed point theorem for multimaps.

• Journal of the Korean Mathematical Society
• /
• v.39 no.3
• /
• pp.387-395
• /
• 2002

In [11] Kim obtained fixed point theorems for maps defined on some “locally G-convex”subsets of a generalized convex space. Theorem 2 in Kim's article determines us to introduce, in this paper, the notion of K-G-convex space. In this framework we obtain fixed point theorems, section properties and minimax inequalities.