• Bulletin of the Korean Mathematical Society
• /
• v.54 no.4
• /
• pp.1347-1359
• /
• 2017

The purpose of this paper is to give some new iterative methods for finding a common zero of a finite family of monotone operators in Hilbert spaces. We also give the applications of the obtained result for the convex feasibility problem and constrained convex optimization problem in Hilbert spaces.

• Kyungpook Mathematical Journal
• /
• v.49 no.2
• /
• pp.203-209
• /
• 2009

In this paper we study some spectral properties of the class (y) operators and we will investigate on the relation between this class and other usual classes of operators.

• Bulletin of the Korean Mathematical Society
• /
• v.56 no.1
• /
• pp.187-200
• /
• 2019

Truncated Hankel operators are compressions of classical Hankel operators to model spaces. In this paper we describe matrix representations of truncated Hankel operators on finite-dimensional model spaces. We then show that the obtained descriptions hold also for some infinite-dimensional cases.

• Communications of the Korean Mathematical Society
• /
• v.12 no.3
• /
• pp.561-569
• /
• 1997

In this paper we shall characterize a finite triangular operator matrix with M-hyponormal operators on main diagonal. This shows in particualr that such an operator is subscalar operator. As a corollary, we get that every algebraic operator is subscalar.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.585-590
• /
• 2016

Suppose $T_{\varphi}$ is a 2-hyponormal Toeplitz operator whose self-commutator has rank $n{\geq}1$. If $H_{\bar{\varphi}}(ker[T^*_{\varphi},T_{\varphi}])$ contains a vector $e_n$ in a canonical orthonormal basis $\{e_k\}_{k{\in}Z_+}$ of $H^2({\mathbb{T}})$, then ${\varphi}$ should be an analytic function of the form ${\varphi}=qh$, where q is a finite Blaschke product of degree at most n and h is an outer function.

• East Asian mathematical journal
• /
• v.36 no.5
• /
• pp.571-581
• /
• 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 the Korean Society of Fisheries and Ocean Technology
• /
• v.42 no.1
• /
• pp.44-53
• /
• 2006

The expansion of near shore aquaculture is feasibility of moving aquaculture facilities into the open ocean. Numerical modeling technique using finite element method was used to enable the optimum design and evaluation of submersible aquaculture cage system. The characteristics of mooring loads response in mooring lines under waves and current and their response amplitude operators were calculated for single and three point mooring configuration at the surface condition and submerged one. The static mooring loads without wave and current loading were similar for both the surface and submerged configuration. It was calculated that three point mooring was more adequate than single point mooring for the mooring configuration of submersible aquaculture cage system. The wave induced response amplitude operators for the single point mooring configuration with the influence of currents were identical to those without the influence of currents.

• Communications of the Korean Mathematical Society
• /
• v.31 no.3
• /
• pp.549-565
• /
• 2016

A Hilbert space operator $T{\in}{\mathfrak{B}}(\mathfrak{H})$ is said to be n-*-paranormal, $T{\in}C(n)$ for short, if ${\parallel}T^*x{\parallel}^n{\leq}{\parallel}T^nx{\parallel}\;{\parallel}x{\parallel}^{n-1}$ for all $x{\in}{\mathfrak{H}}$. We proved some properties of class C(n) and we proved an asymmetric Putnam-Fuglede theorem for n-*-paranormal. Also, we study some invariants of Weyl type theorems. Moreover, we will prove that a class n-* paranormal operator is finite and it remains invariant under compact perturbation and some orthogonality results will be given.

• Bulletin of the Korean Mathematical Society
• /
• v.52 no.3
• /
• pp.851-864
• /
• 2015

In this paper, we study the generalized Littlewood-Paley operators. It is shown that the generalized g-function, Lusin area function and $g^*_{\lambda}$-function on any BMO function are either infinite everywhere, or finite almost everywhere, respectively; and in the latter case, such operators are bounded from BMO($\mathbb{R}^n$) to BLO($\mathbb{R}^n$), which improve and generalize some previous results.

• Communications of the Korean Mathematical Society
• /
• v.32 no.4
• /
• pp.1025-1031
• /
• 2017

We prove the uniqueness of solutions for the boundary value problem of certain nonlinear elliptic operators in the setting: Given any continuous function f on the p-harmonic boundary of a complete Riemannian manifold, there exists a unique solution of certain nonlinear elliptic operators, which is a limit of a sequence of solutions of the operators with finite energy in the sense of supremum norm, on the manifold taking the same boundary value at each p-harmonic boundary as that of f.