• 대한수학회논문집
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• 제34권4호
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• pp.1201-1222
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• 2019

In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권4호
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• pp.297-314
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• 2021

This manuscript is divided into three segments. In the first segment, we formulate a unique common fixed point theorem satisfying generalized Meir-Keeler contraction on partially ordered metric spaces and also give an example to demonstrate the usability of our result. In the second segment of the article, some common coupled fixed point results are derived from our main results. In the last segment, we investigate the solution of some periodic boundary value problems. Our results generalize, extend and improve several well-known results of the existing literature.

• 대한수학회보
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• 제60권1호
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• pp.33-46
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• 2023

Geodesic orbit spaces are homogeneous Finsler spaces whose geodesics are all orbits of one-parameter subgroups of isometries. Such Finsler spaces have vanishing S-curvature and hold the Bishop-Gromov volume comparison theorem. In this paper, we obtain a complete description of invariant (α₁, α₂)-metrics on spheres with vanishing S-curvature. Also, we give a description of invariant geodesic orbit (α₁, α₂)-metrics on spheres. We mainly show that a Sp(n + 1)-invariant (α₁, α2)-metric on S⁴ⁿ⁺³ = Sp(n + 1)/Sp(n) is geodesic orbit with respect to Sp(n + 1) if and only if it is Sp(n + 1)Sp(1)-invariant. As an interesting consequence, we find infinitely many Finsler spheres with vanishing S-curvature which are not geodesic orbit spaces.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제31권1호
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• pp.83-102
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• 2024

In this paper, first we establish a unique common fixed point theorem satisfying new contractive condition on partially ordered non-Archimedean fuzzy metric spaces and give an example to support our result. By using the result established in the first section of the manuscript, we formulate a unique common coupled fixed point theorem and also give an example to validate our result. In the end, we study the existence of solution of integral equation to verify our hypothesis. These results generalize, improve and fuzzify several well-known results in the existing literature.

• 대한수학회보
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• 제41권3호
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• pp.457-464
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• 2004

Let X be a Banach space and Z a closed subspace of a Banach space Y. Denote by Ｌ(X, Y) the space of all bounded linear operators from X to Y and by Ｋ(X, Y) its subspace of compact linear operators. Using Hahn-Banach extension operators corresponding to ideal projections, we prove that if either $X^{**}$ or $Y^{*}$ has the Radon-Nikodym property and Ｋ(X, Y) is an M-ideal (resp. an HB-subspace) in Ｌ(X, Y), then Ｋ(X, Z) is also an M-ideal (resp. HB-subspace) in Ｌ(X, Z). If Ｌ(X, Y) has property SU instead of being an M-ideal in Ｌ(X, Y) in the above, then Ｋ(X, Z) also has property SU in Ｌ(X, Z). If X is a Banach space such that $X^{*}$ has the metric compact approximation property with adjoint operators, then M-ideal (resp. HB-subspace) property of Ｋ(X, Y) in Ｌ(X, Y) is inherited to Ｋ(X, Z) in Ｌ(X, Z).

• 호남수학학술지
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• 제31권2호
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• pp.185-201
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• 2009

Let M be a real hypersurface with almost contact metric structure $({\phi},{\xi},{\eta},g)$ of a nonflat complex space form whose structure Jacobi operator $R_{\xi}=R({\cdot},{\xi}){\xi}$ is ${\xi}$-parallel. In this paper, we prove that the condition ${\nabla}_{\xi}R_{\xi}=0$ characterize the homogeneous real hypersurfaces of type A in a complex projective space $P_n{\mathbb{C}}$ or a complex hyperbolic space $H_n{\mathbb{C}}$ when $g({\nabla}_{\xi}{\xi},{\nabla}_{\xi}{\xi})$ is constant.

• Journal of applied mathematics & informatics
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• 제11권1_2호
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• pp.391-399
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• 2003

Let (X,S,$\mu$) be a measure space and M be the vector space of all real valued S-measurable functions defined on (X,S,$\mu$). For $E\;{\in}\;S$ with $\mu(E)\;<\;{\infty}$, $d_E$ is a pseudometric on M. With the notion of D = {$d_E$\mid$E\;{\in}\;S,\mu(E)\;<\;{\infty}$}, in this paper we investigate some topological structure T of M. Indeed, we shall show that it is possible to define a complete invariant metric on M which is compatible with the topology T on M.

• 대한수학회지
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• 제58권6호
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• pp.1407-1419
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• 2021

The Iwasawa decomposition NAK of the Lie group G = SO₀(2, 1) with a left invariant metric produces Riemannian submersions G → N\G, G → A\G, G → K\G, and G → NA\G. For each of these, we calculate the curvature of the base space and the lifting of a simple closed curve to the total space G. Especially in the first case, the base space has a constant curvature 0; the holonomy displacement along a (null-homotopic) simple closed curve in the base space is determined only by the Euclidean area of the region surrounded by the curve.

• 한국정보과학회논문지:컴퓨팅의 실제 및 레터
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• 제16권6호
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• pp.648-653
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• 2010

비계량 다차원 척도법은 개체들 간의 비유사성이 비계량으로 주어져 개체들 간의 거리 개념을 설정하기 어려운 경우에 개체들을 유클리드 공간 상으로 사상하여 개체 간의 관련성을 연구하는 방법으로 지역 최적치가 많은 최적화 문제로 간주할 수 있다. 비계량 다차원 척도법을 위한 기존의 알고리즘은 최대 경사법을 사용함으로 일단 지역 최적치에 도달하면 더 이상 향상된 해를 찾기 어렵다는 단점이 있다. 이러한 단점을 해결하기 위하여 본 논문에서는 담금질 방법을 비계량 다차원 척도법에 접목하여 지역 최적치에 빠지지 않고 전역 최적치를 효율적으로 찾을 수 있는 새로운 비계량 다차원 척도법 알고리즘을 제안하였다. 제안한 알고리즘을 벤치마킹 문제에 적용하고 실험을 통하여 기존 알고리즘과 비교 분석한 결과, 제안한 알고리즘은 기존 알고리즘 대비 0.7%에서 3.2%의 향상률을 보였다. 또한 통계적 가설 검정을 통하여 제안한 알고리즘의 우수성을 입증하였다.

• 한국정보과학회:학술대회논문집
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• 한국정보과학회 2011년도 한국컴퓨터종합학술대회논문집 Vol.38 No.1(C)
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• pp.112-114
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• 2011

On multimedia databases, in order to realize the fast access method, indexing methods for the multidimension data space are used. However, since it is a premise to use the Euclid distance as the distance measure, this method lacks in flexibility. On the other hand, there are metric indexing methods which require only to satisfy distance axiom. Since metric indexing methods can also apply for distance measures other than the Euclid distance, these methods have high flexibility. This paper proposes an improved method of VP-tree which is one of the metric indexing methods. VP-tree follows the node which suits the search range from a route node at searching. And distances between a query and all objects linked from the leaf node which finally arrived are computed, and it investigates whether each object is contained in the search range. However, search speed will become slow if the number of distance calculations in a leaf node increases. Therefore, we paid attention to the candidates selection method using the triangular inequality in a leaf node. As the improved methods, we propose a method to use the nearest neighbor object point for the query as the datum point of the triangular inequality. It becomes possible to make the search range smaller and to cut down the number of times of distance calculation by these improved methods. From evaluation experiments using 10,000 image data, it was found that our proposed method could cut 5%~12% of search time of the traditional method.