• East Asian mathematical journal
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• v.36 no.5
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• pp.571-581
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• 2020

In this paper, an equilibrium problems involving a finite family of maximal monotone operators and inverse-strongly monotone operators are introduced and investigated. A strong convergence theorem of common solutions is obtained in Hilbert spaces.

• Journal of applied mathematics & informatics
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• v.28 no.1_2
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• pp.451-463
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• 2010

In this paper, we introduce and study a class of completely generalized quasi-variational inclusions with fuzzy mappings. A new iterative algorithm for finding the approximate solutions and the convergence criteria of the iterative sequences generated by the algorithm are also given. These results of existence, algorithm and convergence generalize many known results.

• Bulletin of the Korean Mathematical Society
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• v.50 no.6
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• pp.2071-2077
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• 2013

In this paper we consider the existence of smooth conics on a general hypersurface of degree d in $\mathbb{P}^n$.

• East Asian mathematical journal
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• v.15 no.2
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• pp.301-312
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• 1999

In this paper, we study the nonlinear ergodic retraction theorems for an asymptotically nonexpansive semigroup with nonconvex and nonclosed domains in Hilbert spaces.

• Communications of the Korean Mathematical Society
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• v.16 no.3
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• pp.371-383
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• 2001

In this survey article, we shall introduce the applications of the theory of reproducing kernels to inverse problems. At the same time, we shall present some operator versions of our fundamental general theory for linear transforms in the framework of Hilbert spaces.

• Bulletin of the Korean Mathematical Society
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• v.36 no.2
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• pp.351-355
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• 1999

If ($H_1$, $H_2$) is a doubly commuting pair of hyponormal operators on a Hilbert spaces H, then there exists a commuting pair ($T_1$,$T_1$) of contractions on H such that $H_i$=$H_i^*$$T_i$ for each i=1,2.

• Bulletin of the Korean Mathematical Society
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• v.60 no.3
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• pp.845-848
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• 2023

Erratum/Addendum to the paper "Biisometric operators and biorthogonal sequences" [Bull. Korean Math. Soc. 56 (2019), No. 3, pp. 585-596].

• Bulletin of the Korean Mathematical Society
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• v.54 no.2
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• pp.485-495
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• 2017

The aim of this paper is twofold. Firstly, we introduce the concept of semi-partial isometry in a Banach algebra and carry out a comparison and a classification study for this concept. In particular, we show that in the context of $C^*$-algebras this concept coincides with the notion of partial isometry. Our results encompass several earlier ones concerning partial isometries in Hilbert spaces, Banach spaces and $C^*$-algebras. Finally, we study the notion of (m, p)-semi partial isometries.

• Communications of the Korean Mathematical Society
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• v.38 no.3
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• pp.821-835
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• 2023

Hankel operators and their variants have abundant applications in numerous fields. For a non-zero complex number r, the r-Hankel operators on a Hilbert space 𝓗 define a class of one such variant. This article introduces and explores some properties of two other variants of Hankel operators namely k^th-order (C, r)-Hankel operators and k^th-order (R, r)-Hankel operators (k ≥ 2) which are closely related to r-Hankel operators in such a way that a k^th-order (C, r)-Hankel matrix is formed from r^k-Hankel matrix on deleting every consecutive (k - 1) columns after the first column and a k^th-order (R, r^k)-Hankel matrix is formed from r-Hankel matrix if after the first column, every consecutive (k - 1) columns are deleted. For |r| ≠ 1, the characterizations for the boundedness of these operators are also completely investigated. Finally, an appropriate approach is also presented to extend these matrices to two-way infinite matrices.

• Honam Mathematical Journal
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• v.23 no.1
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• pp.51-57
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• 2001

Let $\mathcal{B}(H)$ and $\mathcal{B}(K)$ denote the algebras of all bounded linear operators on Hilbert spaces $\mathcal{H}$ and $\mathcal{K}$, respectively. We show that if ${\phi}:\mathcal{B}(H){\rightarrow}\mathcal{B}(K)$ is an additive mapping satisfying ${\phi}({\mid}A{\mid}^2)={\mid}{\phi}(A){\mid}^2$ for every $A{\in}\mathcal{B}(H)$, then there exists a mapping ${\psi}$ defined by ${\psi}(A)={\phi}(I){\phi}(A)$, ${\forall}A{\in}\mathcal{B}(H)$ such that ${\psi}$ is the sum of $two^*$-homomorphisms one of which C-linear and the othere C-antilinear. We will also study some conditions implying the injective and rank-preserving of ${\psi}$.