• 한국수학교육학회지시리즈B:순수및응용수학
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• 제23권1호
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• pp.35-51
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• 2016

We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G : X² → X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.

• 대한수학회보
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• 제55권4호
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• pp.1231-1240
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• 2018

In this paper, we characterize the conformal transformations between two almost regular (${\alpha},{\beta}$)-metrics. Suppose that F is a non-Riemannian (${\alpha},{\beta}$)-metric and is conformally related to ${\widetilde{F}}$, that is, ${\widetilde{F}}=e^{{\kappa}(x)}F$, where ${\kappa}:={\kappa}(x)$ is a scalar function on the manifold. We obtain the necessary and sufficient conditions of the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature. Further, when both F and ${\widetilde{F}}$ are regular, the conformal transformation between F and ${\widetilde{F}}$ preserving the mean Landsberg curvature must be a homothety.

• Journal of Information Processing Systems
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• 제16권5호
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• pp.1105-1112
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• 2020

Gait recognition, as a promising biometric, can be used in video-based surveillance and other security systems. However, due to the complexity of leg movement and the difference of external sampling conditions, gait recognition still faces many problems to be addressed. In this paper, an improved convolutional neural network (CNN) based on Gabor filter is therefore proposed to achieve gait recognition. Firstly, a gait feature extraction layer based on Gabor filter is inserted into the traditional CNNs, which is used to extract gait features from gait silhouette images. Then, in the process of gait classification, using the output of CNN as input, we utilize metric learning techniques to calculate distance between two gaits and achieve gait classification by k-nearest neighbors classifiers. Finally, several experiments are conducted on two open-accessed gait datasets and demonstrate that our method reaches state-of-the-art performances in terms of correct recognition rate on the OULP and CASIA-B datasets.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권3호
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• pp.181-198
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• 2013

C. Vetro [4] gave the concept of weak non-Archimedean in fuzzy metric space. Using the same concept for Menger PM spaces, Mishra et al. [22] proved the common fixed point theorem for six maps, Also they introduced semi-compatibility. In this paper, we generalized the theorem [22] for family of maps and proved the common fixed point theorems using the pair of semi-compatible and reciprocally continuous maps for one pair and R-weakly commuting maps for another pair in Menger WNAPM-spaces. Our results extends and generalizes several known results in metric spaces, probabilistic metric spaces and the similar spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제4권2호
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• pp.137-144
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• 1997

In this paper we consider covering problems in spherical geometry. Let $cov_q{S_1}^n$ be the smallest radius of q equal metric balls that cover n-dimensional unit sphere ${S_1}^n$. We show that $cov_q{S_1}^n\;=\;\frac{\pi}{2}\;for\;2\leq\;q\leq\;n+1$ and $\pi-arccos(\frac{-1}{n+1})$ for q = n ＋ 2. The configuration of centers of balls realizing $cov_q{S_1}^n$ are established, simultaneously. Moreover, some properties of $cov_{q}$X for the compact metric space X, in general, are proved.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제8권2호
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• pp.153-162
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• 2001

In this Paper, the notion of $\varepsilon$-Birkhoff orthogonality introduced by Dragomir [An. Univ. Timisoara Ser. Stiint. Mat. 29(1991), no. 1, 51-58] in normed linear spaces has been extended to metric linear spaces and a decomposition theorem has been proved. Some results of Kainen, Kurkova and Vogt [J. Approx. Theory 105 (2000), no. 2, 252-262] proved on e-near best approximation in normed linear spaces have also been extended to metric linear spaces. It is shown that if (X, d) is a convex metric linear space which is pseudo strictly convex and M a boundedly compact closed subset of X such that for each $\varepsilon$>0 there exists a continuous $\varepsilon$-near best approximation $\phi$ : X → M of X by M then M is a chebyshev set .

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권4호
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• pp.269-276
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• 2013

We find an explicit $C^{\infty}$-continuous path of Riemannian metrics $g_t$ on the 4-d hyperbolic space $\mathbb{H}^4$, for $0{\leq}t{\leq}{\varepsilon}$ for some number ${\varepsilon}$ > 0 with the following property: $g_0$ is the hyperbolic metric on $\mathbb{H}^4$, the scalar curvatures of $g_t$ are strictly decreasing in t in an open ball and $g_t$ is isometric to the hyperbolic metric in the complement of the ball.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제25권4호
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• pp.279-295
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• 2018

We study the existence and uniqueness of fixed point for isotone mappings of any number of arguments under Geraghty-type contraction on a complete metric space endowed with a partial order. As an application of our result we study the existence and uniqueness of the solution to a nonlinear Fredholm integral equation. Our results generalize, extend and unify several classical and very recent related results in the literature in metric spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권4호
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• pp.369-399
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• 2022

In the last few decades, a lot of generalizations of the Banach contraction principle have been introduced. In this paper, we present the notion of (𝜙, F)-contraction in generalized asymmetric metric spaces and we investigate the existence of fixed points of such mappings. We also provide some illustrative examples to show that our results improve many existing results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권2호
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• pp.127-132
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• 2003

The object of this paper is to extend and generalize the work of Brosowski ［Fixpunktsatze in der approximationstheorie. Mathematica Cluj 11 (1969), 195-200］, Hicks & Humphries ［A note on fixed point theorems. J. Approx. Theory 34 (1982), 221-225］, Khan & Khan ［An extension of Brosowski-Meinardus theorem on invariant approximation. Approx. Theory Appl. 11 (1995), 1-5］ and Singh ［An application of a fixed point theorem to approximation theory J. Approx. Theory 25 (1979), 89-90; Application of fixed point theorem in approximation theory. In: Applied nonlinear analysis (pp. 389-394). Academic Press, 1979］ in metric spaces having convex structure, and in metric linear spaces having strictly monotone metric.