• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권1호
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• pp.1-13
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• 2021

In this note we use a generalization of coincidence point(a property which was defined by [1] in symmetric spaces) to prove common fixed point theorem on S-metric spaces for weakly compatible maps. Also the results are used to achieve the solution of an integral equation and the bounded solution of a functional equation in dynamic programming.

• Journal of applied mathematics & informatics
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• 제22권1_2호
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• pp.411-424
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• 2006

The purpose of this paper, using the idea of intuitionistic fuzzy set due to Atanassov [2], we define the notion of intuitionistic fuzzy metric spaces (see, [1]) due to Kramosil and Michalek [17] and Jungck's common fixed point theorem ([11]) is generalized to intuitionistic fuzzy metric spaces. Further, we first formulate the definition of weakly commuting and R-weakly commuting mappings in intuitionistic fuzzy metric spaces and prove the intuitionistic fuzzy version of Pant's theorem ([21]).

• 대한수학회논문집
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• 제27권1호
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• pp.117-128
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• 2012

Using the concept of a g-monotone mapping we prove some common fixed point theorems for g-non-decreasing mappings which satisfy some generalized nonlinear contractions in partially ordered complete quasi b-metric spaces. The new theorems are generalizations of very recent fixed point theorems due to L. Ciric, N. Cakic, M. Rojovic, and J. S. Ume, [Monotone generalized nonlinear contractions in partailly ordered metric spaces, Fixed Point Theory Appl. (2008), article, ID-131294] and R. P. Agarwal, M. A. El-Gebeily, and D. O'Regan [Generalized contractions in partially ordered metric spaces, Appl. Anal. 87 (2008), 1-8].

• 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.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.719-729
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• 2023

In this article, we present a new notion called "extended metric spaces of type (φ, ρ)" as a generalization of extended b-metric spaces. Also, we establish a fixed point result of a Reich-type contraction on an extended metric space of type (φ, ρ). We also provide several examples to demonstrate the significance of the established results.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제20권1호
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• pp.11-23
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• 2013

In this paper, we obtain a common fixed point theorem for multivalued mappings in a complete Menger $\mathcal{L}$-fuzzy metric space. $\mathcal{L}$-fuzzy metric space is a generalization of fuzzy metric spaces and intuitionistic fuzzy metric spaces. We extend and generalize the results of Kubiaczyk and Sharma [24], Sharma, Kutukcu and Rathore [34].

• Korean Journal of Mathematics
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• 제20권3호
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• pp.353-360
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• 2012

In this paper we introduce the property (C), which is a cone metric extension of the usual metric property (E,A) and consider fixed point theorems for generalized contractive mappings under suitable conditions in cone metric spaces without normal cones.

• East Asian mathematical journal
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• 제37권1호
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• pp.19-32
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• 2021

We estimate the Bergman metric of the exponentially weighted Bergman space and prove many different geometric characterizations for related Bloch spaces. In particular, we prove that the Bergman metric of the exponentially weighted Bergman space is comparable to some Poincaré type metric.

• 대한수학회보
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• 제43권2호
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• pp.425-441
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• 2006

We have two concepts of Douglas spaces and Lands-berg spaces as generalizations of Berwald spaces. S. Bacso gave the definition of a weakly-Berwald space [2] as another generalization of Berwald spaces. In the present paper, we find the conditions that the Finsler space with an (${\alpha},{\beta}$)-metric be a weakly-Berwald space and the Finsler spaces with some special (${\alpha},{\beta}$)-metrics be weakly-Berwald spaces, respectively.

• 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.