• 충청수학회지
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• 제34권3호
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• pp.259-269
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• 2021

We shall study the following. Let 𝜙 be an expansive flow on a compact TVS-cone metric space (X, d). First, we give some equivalent ways of defining expansiveness. Second, we show that expansiveness is conjugate invariance. Finally, we prove that lim sup ${\frac{1}{t}}$ log v(t) ≤ h(𝜙), where v(t) denotes the number of closed orbits of 𝜙 with a period 𝜏 ∈ [0, t] and h(𝜙) denotes the topological entropy. Remark that in 1972, R. Bowen and P. Walters had proved this three statements for an expansive flow on a compact metric space [?].

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.289-308
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• 2022

In this paper, we introduce the concept of M^*-metric spaces and how much the M^*-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M^*-metric spaces. Also, we investigate some types of convergence associated with M^*-metric spaces. Some common fixed point for contraction and generalized contraction mappings in M^*-metric spaces. Our work has been supported by many examples and an application.

• East Asian mathematical journal
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• 제27권3호
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• pp.273-288
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• 2011

In this paper, we prove some common fixed point theorem for two nonlinear mappings in complete $\mathcal{M}$-fuzzy metric spaces. Our main results improved versions of several fixed point theorems in complete fuzz metric spaces.

• 대한수학회지
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• 제48권1호
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• pp.63-82
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• 2011

On the hyperbolic space $D^n$, codimension-one totally geodesic foliations of class $C^k$ are classified. Except for the unique parabolic homogeneous foliation, the set of all such foliations is in one-one correspondence (up to isometry) with the set of all functions z : [0, $\pi$] $\rightarrow$ $S^{n-1}$ of class $C^{k-1}$ with z(0) = $e_1$ = z($\pi$) satisfying |z'(r)| ${\leq}1$ for all r, modulo an isometric action by O(n-1) ${\times}\mathbb{R}{\times}\mathbb{Z}_2$. Since 1-dimensional metric foliations on $D^n$ are always either homogeneous or flat (that is, their orthogonal distributions are integrable), this classifies all 1-dimensional metric foliations as well. Equations of leaves for a non-trivial family of metric foliations on $D^2$ (called "fifth-line") are found.

• 충청수학회지
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• 제35권3호
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• pp.255-267
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• 2022

Uniform space is a generalization of metric space. The main purpose of this paper is to extend several results contained in [5, 6] which have for an expansive homeomorphism with the pseudo orbit tracing property(POTP in short) on a compact metric space (X, d) for an expansive homeomorphism with the POTP on a compact uniform space (X, 𝒰). we characterize stable and unstable sets, sink and source and saddle, recurrent points for an expansive homeomorphism which has the POTP on a compact uniform space (X, 𝒰).

• Journal of applied mathematics & informatics
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• 제40권5_6호
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• pp.831-842
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• 2022

In this work we classified translation invariant surfaces with zero Gaussian curvature in the 3-dimensional Sol Lie group endowed with Lorentzian metric.

• 대한수학회지
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• 제35권1호
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• pp.165-175
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• 1998

We give a generalization of the selection theorem of Ben-El-Mechaiekh and Oudadess to complete LD-metric spaces with the aid of the notion of n-connectedness. Our new selection theorem is used to obtain new results of fixed points and coincidence points for compact lower semicontinuous set-valued maps with closed values consisting of D-sets in a complete LD-metric space.

• Nonlinear Functional Analysis and Applications
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• 제26권5호
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• pp.949-959
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• 2021

In this paper, some fixed point theorems for new type of (𝜉, 𝛽)-expansive mappings of type (S) and type (T) using control function and 𝛽-admissible function in 𝒢-metric spaces are proved. Further, we prove certain fixed point results by relaxing the continuity condition.

• 대한전기학회논문지:시스템및제어부문D
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• 제50권7호
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• pp.350-353
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• 2001

In general, the Least Square Error method is used for signal classification to measure distance in the $l^2$ metric or the $L^2$ metric space. A defect of the Least Square Error method is that it does not classify properly some waveforms, which is due to the property of the Least Square Error method: the global analysis. This paper proposes a new linear operator, the Integra-Normalizer, that removes the problem. The Integra-Normalizer possesses excellent property that measures the degree of relative similarity between signals by expanding the functional space with removing the restriction on the functional space inherited by the Least Square Error method. The Integra-Normalizer shows superiority to the Least Square Error method in measuring the relative similarity among one dimensional waveforms.

• 대한수학회지
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• 제33권4호
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• pp.891-908
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• 1996

Let (X,d) be a metric space and let T be a mapping from X into itself. We say that a metric space (X,d) is T-orbitally complete if every Cauchy sequence of the form ${T^{n_i}x}_{i \in N}$ for $x \in X$ converges to a point in X.