• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.345-350
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• 2015

In the paper we prove a uniqueness theorem which improves and generalizes a number of uniqueness theorems for meromorphic functions related to Nevanlinna's five value theorem.

• Journal of the Korean Mathematical Society
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• v.42 no.2
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• pp.335-351
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• 2005

This paper concerns the relation between the degree and the projective dimension of linear systems on curves. We generalize Clifford's theorem and its improvement by Coppens and G. Martens and classify the special curves for our problem, and estimate their gonality.

• Journal of the Chungcheong Mathematical Society
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• v.1 no.1
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• pp.3-6
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• 1988

In a recent paper, Parida and Sen obtained a variational-like inequality. In this note, we obtain another variational-like inequality using Fan's minimax inequality [1] and Michael's selection theorem [2]. Also we generalize the Parida-Sen theorem in Banach spaces.

• Journal of Integrative Natural Science
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• v.12 no.2
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• pp.44-46
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• 2019

In this paper, we study a ratio variation of Nicomachus' theorem by computing ${\sum\limits_{k=1}^{n}}[rk]$ and ${\sum\limits_{k=1}^{n}}[rk]^3$, where r is a rational number.

• Bulletin of the Korean Mathematical Society
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• v.36 no.4
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• pp.655-660
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• 1999

Let R be an integral domain with identity. In this paper we will show that if R is integrally closed or if t-dim $R{\leq}1$, then R[{$X_{\alpha}$}] satisfies the principal ideal theorem for each family {$X_{\alpha}$} of algebraically independent indeterminates if and only if R is an S-domain and it satisfies the principal ideal theorem.

• Korean Journal of Mathematics
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• v.24 no.4
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• pp.693-722
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• 2016

In this paper, we characterize the support for the Dunkl transform on the generalized Lebesgue spaces via the Dunkl resolvent function. The behavior of the sequence of $L^p_k$-norms of iterated Dunkl potentials is studied depending on the support of their Dunkl transform. We systematically develop real Paley-Wiener theory for the Dunkl transform on ${\mathbb{R}}^d$ for distributions, in an elementary treatment based on the inversion theorem. Next, we improve the Roe's theorem associated to the Dunkl operators.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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• pp.657-663
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• 1996

In this paper we give some conditions under which the Weyl spectrum of an operator satisfies the spectral mapping theorem for analytic functions. Also we show that Weyl's theorem holds for p(T) where T is an operator of M-power class (N) and p is a polynomial on a neighborhood of $\sigam(T)$. Finally we answer an old question of Oberai.

• Honam Mathematical Journal
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• v.29 no.4
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• pp.577-588
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• 2007

Bearman's rotation theorem is not only very important in pure mathematics but also plays the key role for various research areas, related to Wiener measure. In 2002, the author and professor Im introduced the concept of analogue of Wiener measure, a kind of generalization of Wiener measure and they presented the several papers associated with it. In this article, we prove a formula on analogue of Wiener measure, similar to the formula in Bearman's rotation theorem.

• Journal of the Korean Mathematical Society
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• v.34 no.3
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• pp.719-730
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• 1997

From a minimax inequality related to admissible multimaps, we deduce generalized versions of lopsided saddle point theorems, fixed point theorems, existence of maximizable linear functionals, the Walras excess demand theorem, and the Gale-Nikaido-Debreu theorem.

• Journal of the Korean Mathematical Society
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• v.45 no.5
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• pp.1297-1310
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• 2008

Main purpose of this paper is to combine the optimal form of Fan's best approximation theorem and Nash's equilibrium existence theorem into a single existence theorem simultaneously. For this, we first prove a general best proximity pair theorem which includes a number of known best proximity theorems. Next, we will introduce a new equilibrium concept for a generalized Nash game with normal form, and as applications, we will prove new existence theorems of Nash equilibrium pairs for generalized Nash games with normal form.