• 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.

• 대한수학회보
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• 제36권2호
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• pp.379-388
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• 1999

In this paper, we introduce a semi-metric on a normed almost linear space X via functional. And we prove that a normed almost linear space X is complete if and only if $V_X$ and $W_X$ are complete when X splits as X=$W_X$ + $V_X$. Also, we prove that the dual space $X^\ast$ of a normed almost linear space X is complete.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권1호
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• pp.25-34
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• 2023

Popa [14] proved the common fixed point theorem using implicit relations. Saluja [17] proved a fixed point theorem on complete partial metric spaces satisfying an implicit relation. In this paper, we prove a fixed point theorem on complete partial metric space satisfying another implicit relation.

• East Asian mathematical journal
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• 제16권2호
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• pp.199-203
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• 2000

We give nine necessary and sufficient conditions for a metric space to be complete.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.581-600
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• 2021

In this paper we obtain a unique common fixed point theorem for four self-maps which are involved in (𝜙, 𝜓)-weak contraction of a partially ordered b-metric space. The necessary condition has been given to a space for the existence of an unique common fixed of the maps. And our work changed conditions and nonlinear contraction, and search for the unique common fixed point of the maps.

• 대한수학회지
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• 제55권6호
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• pp.1359-1380
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• 2018

In this paper, we prove that if a metric measure space satisfies the volume doubling condition and the Hardy type inequality with the same exponent n ($n{\geq}3$), then it has exactly the n-dimensional volume growth. Besides, three interesting applications of this fact have also been given. The first one is that we prove that complete noncompact smooth metric measure space with non-negative weighted Ricci curvature on which the Hardy type inequality holds with the best constant are isometric to the Euclidean space with the same dimension. The second one is that we show that if a complete n-dimensional Finsler manifold of nonnegative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then its flag curvature is identically zero. The last one is an interesting rigidity result, that is, we prove that if a complete n-dimensional Berwald space of non-negative n-Ricci curvature satisfies the Hardy type inequality with the best constant, then it is isometric to the Minkowski space of dimension n.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제29권3호
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• pp.231-244
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• 2022

In this paper, we introduce the notion of rational g-h-ϕ-weak contractions in tripled metric-like spaces and demonstrate common fixed point results for each mappings in 0-σ complete tripled metric-like spaces and some examples and application are given.

• 대한수학회논문집
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• 제25권1호
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• pp.59-68
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• 2010

In this paper, we prove common fixed point theorems for semi-compatible mappings on intuitionistic fuzzy metric space with different some conditions of Park and Kim [10]. This research extended and generalized the results of Singh and Chauhan [14].

• 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.