• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.1087-1095
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• 2023

In this paper, the concept of a weighted b_ν(α)-metric space is introduced as a generalization of the b_ν(s)-metric space and ν-metric space. We prove some fixed point results of the Reich-type contraction in the weighted b_ν(α)-metric space. Furthermore, we generalize Reich's theorem by extending the result to a weighted b_ν(α)-metric space.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.30-33
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• 2007

Park and Kim [4], Grabiec [1] studied a fixed point theorem in fuzzy metric space, and Vasuki [8] proved a common fixed point theorem in a fuzzy metric space. Park, Park and Kwun [6] defined the intuitionistic fuzzy metric space in which it is a little revised in Park's definition. Using this definition, Park, Kwun and Park [5] and Park, Park and Kwun [7] proved a fixed point theorem in intuitionistic fuzzy metric space. In this paper, we will prove a common fixed point theorem for a sequence of mappings in a intuitionistic fuzzy metric space. Our result offers a generalization of Vasuki's results [8].

• Nonlinear Functional Analysis and Applications
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• v.28 no.2
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• pp.571-587
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• 2023

In this paper, we have developed the idea of α-β-ψ-contractive mapping in S-metric space and renamed it α_s-β_s-ψ-contractive mapping. We have proved some results of fixed point present in literature in partially ordered S-metric space using α_s-β_s-admissible and α_s-β_s-ψ-contractive mapping.

• Nonlinear Functional Analysis and Applications
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• v.28 no.4
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• pp.877-886
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• 2023

The first result of this paper is to give a revised proof of Sanatammappa et al.'s recent result in a b-metric space, under appropriate choice of constants without using the continuity of the b-metric. The second is to prove a fixed point theorem under a contraction type condition in an extended b-metric space.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.645-656
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• 2010

In this paper, we prove a common fixed point theorem for four mappings on fuzzy 2-metric spaces. Our result is an extension of results of S. H. Cho [2] to fuzzy 2-metric spaces. Also, it is a generalization of a result of S. Sharma [11].

• Honam Mathematical Journal
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• v.45 no.3
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• pp.491-502
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• 2023

As a generalization of Berwald spaces, we have the ideas of Douglas spaces and Landsberg spaces. S. Bacso defined a weakly-Berwald space as another generalization of Berwald spaces. In 1972, Matsumoto proposed the (α, β) metric, which is a Finsler metric derived from a Riemannian metric α and a differential 1-form β. In this paper, we investigated an important class of (α, β)-metrics of the form $F={\mu}_1\alpha+{\mu}_2\beta+{\mu}_3\frac{\beta^2}{\alpha}$, which is recognized as a special form of the first approximate Matsumoto metric on an n-dimensional manifold, and we obtain the criteria for such metrics to be weakly-Berwald metrics. A Finsler space with a special (α, β)-metric is a weakly Berwald space if and only if B^m_m is a 1-form. We have shown that under certain geometric and algebraic circumstances, it transforms into a weakly Berwald space.

• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.401-419
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• 2022

In this paper, we introduce the notion of partial S-metric space and prove a common fixed point theorem in the respective setting. An example is presented to show the effectiveness of this approach.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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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.

• East Asian mathematical journal
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• v.16 no.2
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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.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.3
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• pp.159-164
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• 2007

Park, Park and Kwun[6] is defined the intuitionistic fuzzy metric space in which it is a little revised from Park[5]. According to this paper, Park, Kwun and Park[11] Park and Kwun[10], Park, Park and Kwun[7] are established some fixed point theorems in the intuitionistic fuzzy metric space. Furthermore, Park, Park and Kwun[6] obtained common fixed point theorem in the intuitionistic fuzzy metric space, and also, Park, Park and Kwun[8] proved common fixed points of maps on intuitionistic fuzzy metric spaces. We prove a fixed point for pair of maps with another method from Park, Park and Kwun[7] in intuitionistic fuzzy metric space defined by Park, Park and Kwun[6]. Our research are an extension of Vijayaraju and Marudai's result[14] and generalization of Park, Park and Kwun[7], Park and Kwun[10].