• East Asian mathematical journal
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• 제23권2호
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• pp.175-195
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• 2007

The object of this paper is to introduce the notion of semi-compatible maps in fuzzy metric spaces, fuzzy 2-metric spaces and fuzzy 3-metric spaces and to establish three common fixed point theorems for these spaces for four self-maps. These results improve, extend and generalize the results of [16]. As an application, these results have been used to obtain translation and generalization of Grabeic's contraction principle in the new settings. All the result presented in this paper are new.

• 대한수학회보
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• 제53권2호
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• pp.399-410
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• 2016

In this paper, we study the relations between the Thurston metric and the hyperbolic metric on a closed surface of genus $g{\geq}2$. We show a rigidity result which says if there is an inequality between the marked length spectra of these two metrics, then they are isotopic. We obtain some inequalities on length comparisons between these metrics. Besides, we show certain distance distortions under conformal graftings, with respect to the $Teichm{\ddot{u}}ller$ metric, the length spectrum metric and Thurston's asymmetric metrics.

• 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.

• Kyungpook Mathematical Journal
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• 제54권1호
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• pp.113-122
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• 2014

In this paper, we introduce S-metric spaces and give their some properties. Also we present a common fixed point theorem for multivalued maps on complete S-metric spaces. The single valued case and an illustrative example are given.

• 대한수학회논문집
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• 제27권2호
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• pp.265-277
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• 2012

In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

• 한국경영과학회:학술대회논문집
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• 한국경영과학회/대한산업공학회 2005년도 춘계공동학술대회 발표논문
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• pp.579-584
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• 2005

A metric is a measure of one factor of a company's performance. The metrics are used to monitor the overall performance of the company for achieving business objectives. Insufficient metrics cannot reflect company's conditions. Therefore, it is important to be equipped with 'good' metrics. This study introduces the concept of metric quality and proposes its dimensions. The study also presents application scenarios that show the role and usefulness of the metric quality.

• 대한수학회보
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• 제57권5호
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• pp.1127-1142
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• 2020

In 2016, the Hurwitz metric was introduced by D. Minda in arbitrary proper subdomains of the complex plane and he proved that this metric coincides with the Poincaré's hyperbolic metric when the domains are simply connected. In this paper, we provide an alternate definition of the Hurwitz metric through which we could define a generalized Hurwitz metric in arbitrary subdomains of the complex plane. This paper mainly highlights various important properties of the Hurwitz metric and the generalized metric including the situations where they coincide with each other.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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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.

• 한국산업정보학회:학술대회논문집
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• 한국산업정보학회 1997년도 추계학술대회 발표논문집:21세기를 향한 정보통신 기술의 전망
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• pp.435-449
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• 1997

In this paper, a new metric, universal metric, is Proposed for sequential decoding of convolutional decoding. The complexity of Fano metric for Fano's sequential decoding algorithm is compared with that of the proposed universal metric. Since the Fano metric assumes that it has previous knowledge of channel transition probability, the complexity of Fano metric increases as the assumed channel error probability does not coincide with the true channel error probability. However, the universal metric dose not require the previous knowledge of the channel transition probability since it is estimated on a branch by branch basis. It is shown that the complexity of universal metric is much less than that of the Fano metric for bursty noisy channel.

• 대한수학회논문집
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• 제33권3호
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• pp.943-960
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• 2018

Our aim is to introduce the notion of a parametric $N_b-metric$ and study some basic properties of parametric $N_b-metric$ spaces. We give some fixed-point results on a complete parametric $N_b-metric$ space. Some illustrative examples are given to show that our results are valid as the generalizations of some known fixed-point results. As an application of this new theory, we prove a fixed-circle theorem on a parametric $N_b-metric$ space.