• East Asian mathematical journal
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• 제18권1호
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• pp.127-136
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• 2002

In this paper we obtain some fixed points theorems of expansive mappings and several necessary and sufficient conditions for the existence of common fixed points of families of self-mappings in metric spaces. Our results generalize and improve the main results of Fisher [1]-[5], Furi-Vignoli [6], $Is\'{e}ki$ [7], Jungck [8], [9], Kashara-Rhoades [10], Liu [13], [14] and Sharma and Strivastava [16].

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제10권3호
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• pp.145-161
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• 2003

Weak commutativity of a pair of maps was introduced by Sessa [On a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(40) (1982),149-153] in fixed point considerations. Thereafter a number of generalizations of this notion has been obtained. The purpose of this paper is to present a brief development of weaker forms of commuting maps, and to obtain two fixed point theorems for noncommuting and noncontinuous maps on noncomplete metric spaces.

• 대한수학회논문집
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• 제15권2호
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• pp.331-338
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• 2000

In the present paper, we investigate a problem in a sym-metric Finsler space, which is a special space. First we prove that if a symmetric space remains to be a symmetric one under the Z-projective change, then the space is of zero curvature. Further we will study W-recurrent space and D-recurrent space under the pro-jective change.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.411-427
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• 2019

The existence, uniqueness and iterative approximations of fixed points for some contractive mappings of integral type defined in complete metric spaces with w-distance are proved. Four examples are given to demonstrate that the results in this paper extend and improve some well-known results in the literature.

• Journal of applied mathematics & informatics
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• 제37권5_6호
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• pp.443-457
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• 2019

Some fixed point theorems and properties of diminishing orbital diameters for a few contractive mappings of integral type in complete metric spaces are proved. Four nontrivial examples are included.

• 대한수학회보
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• 제60권4호
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• pp.1131-1139
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• 2023

In this paper, we introduce the concept of ω-expansive of random map on compact metric spaces 𝓟. Also we introduce the definitions of positively, negatively shadowing property and shadowing property for two-sided RDS. Then we show that if 𝜑 is ω-expansive and has the shadowing property for ω, then 𝜑 is topologically stable for ω.

• 한국실내디자인학회논문집
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• 제21권1호
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• pp.148-158
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• 2012

The objective of this study is to find a possible application of small space utilization of GangSo Housing, so called compact-but-effective housing, through analyzing that of Japanese small housing. We analyze openness of view and flexibility of spaces divided by the physical and architectural aspects as first component and the psychological and interior space aspects as second component. The results showed that Japanese small houses have various unit plan compared to uniformity of Korean houses. Openness of view in Japanese small housing is accomplished by letting in light from the outside using position and shape of the window, looking more spacious using courtyard, void spaces, or sliding door hanging from the ceiling, and creating deception of view using floor-wall plan and appropriate materials. Flexibility of spaces is achieved by combination of first and second components, multipurpose of space and furniture, and variety of storage methods. It is necessary to improve spatial efficiency with consideration of volume-metric planing rather than flat-plane and develop various unit plans to meet residents' needs and demands on compact-but-effective houses.

• 정보처리학회논문지D
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• 제12D권2호
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• pp.233-246
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• 2005

멀티미디어 데이터를 위한 내용기반 검색 서비스의 속도를 증진하기 위해 다차원 색인 기법에 대한 연구가 활발하게 진행되고 있다. 다차원 색인 기법의 하나인 M-트리는 노드의 중심점과 객체간의 상대적 거리를 이용하여 색인을 구성하고, 검색 공간에 포함되는 객체를 액세스하는 기법으로서 노드들은 페이지 단위로 구성되며 하위 엔트리들을 포함할 수 있는 반경, 즉 유사도 거리에 의해 노드의 영역이 표현되어진다. 그러나 이와 같은 노드의 영역 표현에 있어서 노드 색인 공간의 중첩으로 인해 질의 시 검색해야 하는 노드수가 증가하고 이는 거리계산과 디스크 입출력의 횟수를 증가시킨다. 본 논문에서는 M-트리에서 문제가 되고 있는 노드 색인 공간 중첩을 최소화하는 노드 분할 정책을 제안한다. M-트리의 기존 분할 정책들과는 다르게 노드의 가상 중심점을 계산하여 라우팅 객체로 이용하여 노드 색인 공간의 중첩을 최소화하고 노드 안의 엔트리 재분배를 통해 노드의 색인 공간의 크기를 작게 유지하며 밀도 높은 노드를 구성하도록 한다. 실험으로부터 제안된 노드 분한 알고리즘이 라우팅 노드의 색인 공간의 반경을 작게 유지하며 결과적으로는 사용자 질의에 대해 개선된 응답 시간을 제공하는 것으로 판명되었다.

• 대한수학회지
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• 제48권2호
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• pp.397-420
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• 2011

In this paper we study the structure of closed weakly dense ideals in Privalov spaces $N^p$ (1 < p < $\infty$) of holomorphic functions on the disk $\mathbb{D}$ : |z| < 1. The space $N^p$ with the topology given by Stoll's metric [21] becomes an F-algebra. N. Mochizuki [16] proved that a closed ideal in $N^p$ is a principal ideal generated by an inner function. Consequently, a closed subspace E of $N^p$ is invariant under multiplication by z if and only if it has the form $IN^p$ for some inner function I. We prove that if $\cal{M}$ is a closed ideal in $N^p$ that is dense in the weak topology of $N^p$, then $\cal{M}$ is generated by a singular inner function. On the other hand, if $S_{\mu}$ is a singular inner function whose associated singular measure $\mu$ has the modulus of continuity $O(t^{(p-1)/p})$, then we prove that the ideal $S_{\mu}N^p$ is weakly dense in $N^p$. Consequently, for such singular inner function $S_{\mu}$, the quotient space $N^p/S_{\mu}N^p$ is an F-space with trivial dual, and hence $N^p$ does not have the separation property.

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.