• Journal of applied mathematics & informatics
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• v.36 no.1_2
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• pp.69-79
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• 2018

The Euclid metric is well-known and there are many results on the space with that metric. But there are many other metrics which gives more practical and useful results in the plane. In this paper, we introduce new metric function in the plane, which is more useful in city with subway. Finally we generalize to the general metric space and introduce a new metric on ${\mathbb{R}}^n$.

• Journal of applied mathematics & informatics
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• v.16 no.1_2
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• pp.371-381
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• 2004

In this paper, fuzzy metric spaces are redefined, different from the previous ones in the way that fuzzy scalars instead of fuzzy numbers or real numbers are used to define fuzzy metric. It is proved that every ordinary metric space can induce a fuzzy metric space that is complete whenever the original one does. We also prove that the fuzzy topology induced by fuzzy metric spaces defined in this paper is consistent with the given one. The results provide some foundations for the research on fuzzy optimization and pattern recognition.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.971-983
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• 2021

In this paper, we prove common fixed point theorems for six weakly compatible mappings in G-fuzzy metric spaces introduced by Sun and Yang [16] which is actually generalization of G-metric spaces. G-metric spaces coined by Mustafa and Sims [13]. The paper concerns our sustained efforts for the materialization of G-fuzzy metric spaces and their properties. We also exercise the concept of symmetric G-fuzzy metric space, 𝜙-function and weakly compatible mappings. The results present in this paper generalize the well-known comparable results in the literature. We justify our results by suitable examples. Some applications are also given in support of our results.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.753-774
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• 2023

The fundamental aim of the proposed work is to introduce the concept of soft rectangular b-metric spaces, which involves generalizing the notions of rectangular metric spaces and b-metric spaces. Furthermore, an investigation into specific characteristics and topological aspects of the underlying generalization of metric spaces is conducted. Moreover, the research establishes fixed point theorems for mappings that satisfy essential criteria within soft rectangular b-metric spaces. These theorems offer a broader perspective on established results in fixed point theory. Additionally, several congruous examples are presented to enhance the understanding of the introduced spatial framework.

• Journal of Korean Society for Quality Management
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• v.31 no.4
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• pp.239-246
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• 2003

Dynamic robust design has been regarded as the most powerful design methodology for improving product quality, Dynamic SN ratio adopted in dynamic robust design combines two major quality attributes, the variability around the linear function and the slope of the linear function, into a single design metric. The principal shortcoming associated with the dynamic SN ratio is that the metric is independent of designer's preferences for the quality attributes due to priori sets of attribute tradeoff values inherent in it. Therefore, a more rigorous preference­based design metric to accurately capture designer's intent and preference is needed. A new design metric that can be used in dynamic robust design is proposed. The effectiveness of the proposed design metric is examined with the aid of a demonstrative case study and the results are discussed.

• Communications of the Korean Mathematical Society
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• v.24 no.2
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• pp.265-275
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• 2009

The object of the present paper is to study 3-dimensional normal almost contact metric manifolds satisfying certain curvature conditions. Among others it is proved that a parallel symmetric (0, 2) tensor field in a 3-dimensional non-cosympletic normal almost contact metric manifold is a constant multiple of the associated metric tensor and there does not exist a non-zero parallel 2-form. Also we obtain some equivalent conditions on a 3-dimensional normal almost contact metric manifold and we prove that if a 3-dimensional normal almost contact metric manifold which is not a ${\beta}$-Sasakian manifold satisfies cyclic parallel Ricci tensor, then the manifold is a manifold of constant curvature. Finally we prove the existence of such a manifold by a concrete example.

• 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].

• East Asian mathematical journal
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• v.23 no.2
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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.

• The Journal of Korean Institute of Electromagnetic Engineering and Science
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• v.11 no.5
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• pp.731-737
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• 2000

In this paper we propose a decoding algorithm of Ungerboeck TCM/PSK in the concept of Radix-trellis, which has been applied to the decoding of convolutional codes for the high speed decoding. As an example we choose 16-state trellis coded 8-ary PSK. For Radix-4 and Radix-16 trellis decoding, we explain the path metric(PM) and the branch metric(BM) calculation. By using the simulation, we evaluate the bit error rate(BER) performance according to the number of binary digits for I-Q value, PM and BM registers. The proper number of binary digits of each register has been derived.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.563-580
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• 2019

In this paper, we study the strong metric dimension of zero-divisor graph ${\Gamma}(R)$ associated to a ring R. This is done by transforming the problem into a more well-known problem of finding the vertex cover number ${\alpha}(G)$ of a strong resolving graph $G_{sr}$. We find the strong metric dimension of zero-divisor graphs of the ring ${\mathbb{Z}}_n$ of integers modulo n and the ring of Gaussian integers ${\mathbb{Z}}_n$[i] modulo n. We obtain the bounds for strong metric dimension of zero-divisor graphs and we also discuss the strong metric dimension of the Cartesian product of graphs.