• 대한수학회지
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• 제58권1호
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• pp.91-107
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• 2021

A bounded linear operator T on a separable infinite dimensional Banach space X is called strongly hypercyclic if $$X{\backslash}\{0\}{\subseteq}{\bigcup_{n=0}^{\infty}}T^n(U)$$ for all nonempty open sets U ⊆ X. We show that if T is strongly hypercyclic, then so are Tn and cT for every n ≥ 2 and each unimodular complex number c. These results are similar to the well known Ansari and León-Müller theorems for hypercyclic operators. We give some results concerning multiplication operators and weighted composition operators. We also present a result about the invariant subset problem.

• Journal of applied mathematics & informatics
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• 제40권1_2호
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• pp.327-339
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• 2022

In this paper, we introduce arithmetic ${\mathcal{I}}$-statistically convergent sequence space $A{\mathcal{I}}SC$, ${\mathcal{I}}$-lacunary arithmetic statistically convergent sequence space $A{\mathcal{I}}SC_{\theta}$, strongly ${\mathcal{I}}$-lacunary arithmetic convergent sequence space $AN_{\theta}[{\mathcal{I}}]$ and prove some inclusion relations between these spaces. Futhermore, we give ${\mathcal{I}}$-lacunary arithmetic statistical continuity. Finally, we define ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-Cesàro arithmetic summability. Also, we investigate the relationship between the concepts of strongly ${\mathcal{I}}$-Cesàro arithmetic summability, strongly ${\mathcal{I}}$-lacunary arithmetic summability and arithmetic ${\mathcal{I}}$ -statistically convergence.

• 대한수학회논문집
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• 제38권3호
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• pp.741-754
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• 2023

In this paper, we study the existence and nonexistence of solutions for a class of Hamiltonian strongly degenerate elliptic system with subcritical growth $$\left{\array{-{\Delta}_{\lambda}u-{\mu}v={\mid}v{\mid}^{p-1}v&&\text{in }{\Omega},\\-{\Delta}_{\lambda}v-{\mu}u={\mid}u{\mid}^{q-1}u&&\text{in }{\Omega},\\u=v=0&&\text{ on }{\partial}{\Omega},}$$ where p, q > 1 and Ω is a smooth bounded domain in ℝ^N, N ≥ 3. Here Δ_λ is the strongly degenerate elliptic operator. The existence of at least a nontrivial solution is obtained by variational methods while the nonexistence of positive solutions are proven by a contradiction argument.

• Kyungpook Mathematical Journal
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• 제64권1호
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• pp.15-30
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• 2024

In this paper, we focus on partial isometry elements and strongly EP elements on a ring. We construct characterizing equations such that an element which is both group invertible and MP-invertible, is a partial isometry element, or is strongly EP, exactly when these equations have a solution in a given set. In particular, an element a ∈ R^# ∩ R^† is a partial isometry element if and only if the equation x = x(a^†)^*a^† has at least one solution in {a, a#, a^†, a^*, (a^#)^*, (a^†)^*}. An element a ∈ R^#∩R^† is a strongly EP element if and only if the equation (a^†)^*xa^† = xa^†a has at least one solution in {a, a^#, a^†, a^*, (a^#)^*, (a^†)^*}. These characterizations extend many well-known results.

• 대한수학회보
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• 제37권4호
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• pp.755-764
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• 2000

We introduce a new class of functions $H_{\kappa}({\beta})$ which is related to close-to-star functions and we derive a few geometric properties for the class $H_{\kappa}({\beta}),{\;}(2{\leq}k{\kappa}{\leq}4)$.

• 한국자기학회:학술대회 개요집
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• 한국자기학회 2006년도 동계학술연구발표회 및 자성 스핀트로닉스 국제학술대회
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• pp.92-93
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• 2006

• Journal of applied mathematics & informatics
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• 제4권2호
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• pp.563-571
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• 1997

In this paper we define CR(completely reachable), MICR(minimal cyclic refinement)and MACR(maximal cyclic refinement)-Modules. We have obtained equivalent statements for minimal cyclic submodule and maximal cyclic submodule. Also we have obtained necessary and sufficient conditions for a module M with MICR to be cyclic or strongly cyclic.

• 대한수학회지
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• 제54권2호
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• pp.427-440
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• 2017

In this paper, in terms of the notions of strongly copure projective modules and the copure projective dimension cpD(R) of a ring R were defined in [12], we show that a domain R has $cpD(R){\leq}1$ if and only if R is a Gorenstein Dedekind domain.

• Korean Journal of Mathematics
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• 제17권3호
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• pp.331-340
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• 2009

We show the existence of nonconstant periodic solution for the nonlinear Hamiltonian systems with some nonlinearity. We approach the variational method. We use the critical point theory and the variational linking theory for strongly indefinite functional.

• 대한수학회논문집
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• 제11권2호
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• pp.295-301
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• 1996

In this paper we will define correct module and strongly correct module. We can have some basic results about those modules. And we will show that M is a graded correct R-module if and only if $M_e$ is a correct $R_e$-module.