• 충청수학회지
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• 제34권1호
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• pp.55-60
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• 2021

In this paper we deal with the preservation of the periodic shadowing property of induced hyperspatial systems. More precisely, we show that an expansive system has the periodic shadowing property if and only if its induced hyperspatial system has the periodic shadowing property.

• 대한수학회논문집
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• 제37권3호
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• pp.669-679
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• 2022

We provide a characterization of the positive monoids (i.e., additive submonoids of the nonnegative real numbers) that satisfy the finite factorization property. As a result, we establish that positive monoids with well-ordered generating sets satisfy the finite factorization property, while positive monoids with co-well-ordered generating sets satisfy this property if and only if they satisfy the bounded factorization property.

• 대한수학회논문집
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• 제37권4호
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• pp.1249-1258
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• 2022

In this study, we show that the strong exponential limit shadowing property (SELmSP, for short), which has been recently introduced, exists on a neighborhood of a hyperbolic set of a diffeomorphism. We also prove that Ω-stable diffeomorphisms and 𝓛-hyperbolic homeomorphisms have this type of shadowing property. By giving examples, it is shown that this type of shadowing is different from the other shadowings, and the chain transitivity and chain mixing are not necessary for it. Furthermore, we extend this type of shadowing property to positively expansive maps with the shadowing property.

• 충청수학회지
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• 제37권2호
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• pp.75-80
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• 2024

In this paper, we study some dynamics of the uniform limits of sequences in dynamical systems on a noncompact metric space. We show that if a sequence of homeomorphisms on a noncompact metric space has the uniform ergodic shadowing property, then the uniform limit also has the ergodic shadowing property. Then we apply this result to nonwandering maps.

• Korean Journal of Mathematics
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• 제19권3호
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• pp.301-308
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• 2011

In this paper, we define the alternate forms of property ($A_{\kappa}$) and study their implications.

• 대한수학회보
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• 제46권5호
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• pp.1019-1029
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• 2009

We show that every bridge surface of certain types of (1, 1) prime knot has the disjoint curve property. Also we determine when a bridge surface of a pretzel knot of type (.2, 3, n) has the disjoint curve property.

• 대한수학회보
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• 제39권4호
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• pp.665-669
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• 2002

In this paper, we study averaging properties in Banach space. We prove that the convex block Banach-Saks property is equivalent to the reflexivity in a Banach space. And we show that a weakly compact operator is a convex block Banach-Saks operator.

• Korean Journal of Mathematics
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• 제20권4호
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• pp.415-422
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• 2012

In this paper, we define the weak property (${\beta}_{\kappa}$) and get the following strict implications. $$(UC){\Rightarrow}w-({\beta}_1){\Rightarrow}w-({\beta}_2){\Rightarrow}\;{\cdots}\;{\Rightarrow}w-({\beta}_{\infty}){\Rightarrow}(BS)$$.

• 충청수학회지
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• 제33권2호
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• pp.287-292
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• 2020

In this paper, we prove that a distal homeomorphism f of a compact connected metric space X does not have the eventual pseudo orbit tracing property.

• Journal of applied mathematics & informatics
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• 제28권5_6호
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• pp.1519-1525
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• 2010

In this paper, we define property ($D_k$) and get the following strict implications. $$(UC){\Rightarrow}(D_2){\Rightarrow}(D_3){\Rightarrow}{\cdots}{\Rightarrow}(D_{\infty}){\Rightarrow}(BS)$$.