• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.481-486
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• 2010

In this paper, we introduce the concepts of strongly c-convex( strongly c-concave) function, almost c-convex function on preconvex spaces. We investigate the relationships between such concepts and several types of preconvex sets.

• Journal of applied mathematics & informatics
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• v.14 no.1_2
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• pp.185-191
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• 2004

Given a connected graph G, we say that a set EC\;{\subseteq}\;V(G)$ is convex in G if, for every pair of vertices x, $y\;{\in}\;C$, the vertex set of every x - y geodesic in G is contained in C. The convexity number of G is the cardinality of a maximal proper convex set in G. In this paper, we show that every pair k, n of integers with $2\;{\leq}k\;{\leq}\;n\;-\;1$ is realizable as the convexity number and order, respectively, of some connected triangle-free graph, and give a lower bound for the convexity number of k-regular graphs of order n with n > k+1.

• Bulletin of the Korean Mathematical Society
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• v.41 no.3
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• pp.521-540
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• 2004

In this paper, we give a sharp estimate on the cardinality of the set generating the convex hull containing the image of harmonic maps with polynomial growth rate on a certain class of manifolds into a Cartan-Hadamard manifold with sectional curvature bounded by two negative constants. We also describe the asymptotic behavior of harmonic maps on a complete Riemannian manifold into a regular ball in terms of massive subsets, in the case when the space of bounded harmonic functions on the manifold is finite dimensional.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.905-913
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• 2022

We characterize metrizability and submetrizability for point-open, open-point and bi-point-open topologies on C(X, Y), where C(X, Y) denotes the set of all continuous functions from space X to Y ; X is a completely regular space and Y is a locally convex space.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.9
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• pp.1796-1801
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• 2009

This paper is concerned with the problem of delay-dependent robust $H_{\infty}$ filtering for uncertain descriptor systems with time-varying delay. The considering uncertainty is convex compact set of polytoic type. The purpose is the design of a linear filter such that the resulting filtering error descriptor system is regular, impulse-free, and asymptotically stable with $H_{\infty}$ norm bound. By establishing a finite sum inequality based on quadratic terms, a new delay-dependent bounded real lemma (BRL) for delayed descriptor systems is derived. Based on the derived BRL, a robust $H_{\infty}$ filter is designed in terms of linear matrix inequaltity (LMI). Numerical examples are given to illustrate the effectiveness of the proposed method.

• Journal of the Korean Mathematical Society
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• v.46 no.6
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• pp.1151-1164
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• 2009

Let E be a reflexive Banach space with a weakly sequentially continuous duality mapping, C be a nonempty closed convex subset of E, f : C $\rightarrow$C a contractive mapping (or a weakly contractive mapping), and T : C $\rightarrow$ C a nonexpansive mapping with the fixed point set F(T) ${\neq}{\emptyset}$. Let {$x_n$} be generated by a new composite iterative scheme: $y_n={\lambda}_nf(x_n)+(1-{\lambda}_n)Tx_n$, $x_{n+1}=(1-{\beta}_n)y_n+{\beta}_nTy_n$, ($n{\geq}0$). It is proved that {$x_n$} converges strongly to a point in F(T), which is a solution of certain variational inequality provided the sequence {$\lambda_n$} $\subset$ (0, 1) satisfies $lim_{n{\rightarrow}{\infty}}{\lambda}_n$ = 0 and $\sum_{n=0}^{\infty}{\lambda}_n={\infty}$, {$\beta_n$} $\subset$ [0, a) for some 0 < a < 1 and the sequence {$x_n$} is asymptotically regular.