• Kyungpook Mathematical Journal
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• 제61권2호
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• pp.279-308
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• 2021

The purpose of this paper is to introduce a class of contractive pairs of mappings satisfying a Zamfirescu-type inequality, but controlled with altering distance functions and with parameters satisfying the so-called Geraghty condition in the framework of b-metric spaces. For this class of mappings we prove the existence of points of coincidence, the convergence and stability of the Jungck, Jungck-Mann and Jungck-Ishikawa iterative processes and the existence and uniqueness of its common fixed points.

• 대한수학회보
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• 제61권1호
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• pp.281-290
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• 2024

We consider the total scalar curvature functional, and show that if the second variation in the transverse traceless tensor direction is negative, then the metric is Einstein. We also find the relation between the second variation and the Lichnerowicz Laplacian.

• 대한수학회보
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• 제41권4호
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• pp.665-676
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• 2004

In this paper we characterize asymptotic stability via Lyapunov function in general dynamical systems on c-first countable space. We give a family of examples which have first countable but not c-first countable, also c-first countable and locally compact space but not metric space. We obtain several necessary and sufficient conditions for a compact subset M of the phase space X to be asymptotic stability.

• Journal of Computing Science and Engineering
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• 제4권3호
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• pp.225-239
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• 2010

This paper introduces a new approach to modeling relative distance among nodes under a variety of communication rates, due to node's mobility in Mobile Ad-hoc Networks (MANETs). When mobile nodes move to another location, the relative distance of communicating nodes will directly affect the data rate of transmission. The larger the distance between two communicating nodes is, the lower the rate that they can use for transferring data will be. The connection certainty of a link also changes because a node may move closer to or farther away out of the communication range of other nodes. Therefore, the stability of a route is related to connection entropy. Taking into account these issues, this paper proposes a new routing metric for MANETs. The new metric considers both link weight and route stability based on connection entropy. The problem of determining the best route is subsequently formulated as the minimization of an object function formed as a linear combination of the link weight and the connection uncertainty of that link. The simulation results show that the proposed routing metric improves end-to-end throughput and reduces the percentage of link breakages and route reparations.

• 충청수학회지
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• 제30권1호
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• pp.61-66
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• 2017

In this paper, we introduce the notion of persistent actions of finitely generated groups on compact metric spaces and give a necessary condition for a persistent dynamical system to be topologically stable.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제2권2호
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• pp.149-156
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• 1995

In stability theory of polysystems two concepts that playa very important role are the limit set and the prolongational limit set. For the above two concepts, A.Bacciotti and N.Kalouptsidis studied their properties in a locally compact metric space [2]. In this paper we investigate their results in c-first countable space which is more a general space than a metric space.(omitted)

• 대한수학회지
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• 제60권5호
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• pp.1043-1055
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• 2023

In this paper we study a pointwise version of Walters topological stability in the class of homeomorphisms on a compact metric space. We also show that if a sequence of homeomorphisms on a compact metric space is uniformly expansive with the uniform shadowing property, then the limit is expansive with the shadowing property and so topologically stable. Furthermore, we give examples to illustrate our results.

• 대한수학회지
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• 제57권4호
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• pp.935-955
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• 2020

In this paper we present a measurable version of the Smale's spectral decomposition theorem for homeomorphisms on compact metric spaces. More precisely, we prove that if a homeomorphism f on a compact metric space X is invariantly measure expanding on its chain recurrent set CR(f) and has the eventually shadowing property on CR(f), then f has the spectral decomposition. Moreover we show that f is invariantly measure expanding on X if and only if its restriction on CR(f) is invariantly measure expanding. Using this, we characterize the measure expanding diffeomorphisms on compact smooth manifolds via the notion of Ω-stability.

• 충청수학회지
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• 제11권1호
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• pp.73-85
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• 1998

This paper deals with the topological stability of continuous maps. First, the notion of local expansion is given and we show that local expansions of compact metric spaces have the shadowing property. Also, we prove that if a continuous surjective map f is a local homeomorphism and local expansion, then f is topologically stable in the class of continuous surjective maps. Finally, we find homeomorphisms which are not topologically stable.

• 대한수학회지
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• 제56권1호
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• pp.53-65
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• 2019

Recently, Chung and Lee [2] introduced the notion of topological stability for a finitely generated group action, and proved a group action version of the Walters's stability theorem. In this paper, we introduce the concepts of continuous shadowing and continuous inverse shadowing of a finitely generated group action on a compact metric space X with respect to various classes of admissible pseudo orbits and study the relationships between topological stability and continuous shadowing and continuous inverse shadowing property of group actions. Moreover, we introduce the notion of structural stability for a finitely generated group action, and we prove that an expansive action on a compact manifold is structurally stable if and only if it is continuous inverse shadowing.