• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1997년도 추계학술대회 학술발표 논문집
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• pp.69-72
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• 1997

In this papaers, we generalize the usual fuzzy metric on R, the set of all real numbers, and induce the fuzzy metric space(X, d) from a metric space(X, d)

• 충청수학회지
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• 제17권2호
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• pp.111-124
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• 2004

In [4], Dhage proved a result for common fixed point of two self-maps satisfying a contractive condition in D-metric spaces. This note proves a fixed point theorem for five self-maps under weak-compatibility in D-metric space which improves and generalizes the above mentioned result.

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.309-322
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• 2022

In this paper, we introduce the notion of a new generalized type of rational F-contraction mapping. Further, the concept is used to obtain fixed points in a complete b-metric space. We also prove another unique fixed point theorem in the context of b-metric space. Our results are verified with example.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제9권1호
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• pp.1-7
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• 2002

For A bounded subset G of a metric Space (X,d) and $\chi \in X$, let $f_{G}$ be the real-valued function on X defined by $f_{G}$($\chi$)=sup{$d (\chi, g)\in:G$}, and $F(G,\chi)$={$z \in X:sup_{g \in G}d(g,z)=sup_{g \in G}d(g,\chi)+d(\chi,z)$}. In this paper we discuss some properties of the map $f_G$ and of the set $ F(G, \chi)$ in convex metric spaces. A sufficient condition for an element of a convex metric space X to lie in $ F(G, \chi)$ is also given in this pope.

• Journal of applied mathematics & informatics
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• 제27권1_2호
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• pp.351-363
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• 2009

In this paper, we give some new definitions of $D^*$-metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete $D^*$-metric spaces. We get some improved versions of several fixed point theorems in complete $D^*$-metric spaces.

• East Asian mathematical journal
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• 제25권1호
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• pp.107-117
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• 2009

In this paper, we give some new definitions of D-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly compatible mappings in complete D-metric spaces. We get some improved versions of several fixed point theorems in complete D-metric spaces.

• 충청수학회지
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• 제19권1호
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• pp.1-8
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• 2006

In this paper, we obtain some unique common fixed point theorems for four self-maps and pair of maps in D-metric space using orbitally lower semi continuity conditions.

• 대한수학회보
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• 제55권3호
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• pp.967-970
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• 2018

The aim of this paper is to show that there exists a weakly quasisymmetric homeomorphism $f:(X,d){\rightarrow}(Y,d^{\prime})$ between two locally compact non-complete metric spaces such that $f:(X,d_h){\rightarrow}(Y,d^{\prime}_h)$ is not quasi-isometric, where dh denotes the Gromov hyperbolic metric with respect to the metric d introduced by Ibragimov in 2011. This result shows that the answer to the related question asked by Ibragimov in 2013 is negative.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제18권1호
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• pp.13-29
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• 2011

In this paper, we introduce the new concept of ${\omega}-D^*$-distance on a $D^*$-metric space and prove a non-convex minimization theorem which improves the result of Caristi[1], ${\'{C}}iri{\'{c}}$[2], Ekeland[4], Kada et al.[5] and Ume[8, 9].

• Nonlinear Functional Analysis and Applications
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• 제27권2호
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• pp.233-247
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• 2022

In the present manuscript, we employ the concepts of Θ-map and Φ-map to define a strong (𝜃, 𝜙)s-contraction of a map f in a b-metric space (M, d_b). Then we prove and derive many fixed point theorems as well as we provide an example to support our main result. Moreover, we utilize our results to obtain many results in the settings of metric and G-metric spaces. Our results improve and modify many results in the literature.