• Korean Journal of Mathematics
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• v.32 no.1
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• pp.109-120
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• 2024

The aim of this research is to describe lacunary ∆^m-statistically convergent sequences with respect to metrics on generalised metric spaces (g-metric spaces) and to look into the fundamental characteristics of this statistical form of convergence. Also, the relationship between strong summability and lacunary ∆^m-statistical convergence in g-metric space is established at the end.

• Bulletin of the Korean Mathematical Society
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• v.61 no.4
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• pp.897-906
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• 2024

On a Hermitian manifold, the Chern connection can induce a metric connection on the background Riemannian manifold. We call the sectional curvature of the metric connection induced by the Chern connection the Chern sectional curvature of this Hermitian manifold. First, we derive expression of the Chern sectional curvature in local complex coordinates. As an application, we find that a Hermitian metric is Kähler if the Riemann sectional curvature and the Chern sectional curvature coincide. As subsequent results, Ricci curvature and scalar curvature of the metric connection induced by the Chern connection are obtained.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1997.10a
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• pp.69-72
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• 1997

In this papaers, we generalize the usual fuzzy metric on R, the set of all real numbers, and induce the fuzzy metric space(X, d) from a metric space(X, d)

• Communications of the Korean Mathematical Society
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• v.18 no.1
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• pp.87-94
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• 2003

We use geometric properties of Gromov-Hausdorff-convergence to present a way to construct rough but natural invariants of metric geometry.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.05a
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• pp.21-24
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• 2001

In this paper, we investigate some properties of the Skorokhod metric on the space F(R$\^$p/) of upper semicontinuous fuzzy subsets of R$\^$p/ with compact support, which include the continuity of operations, the translation inveriance and convexity.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.9 no.2
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• pp.137-140
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• 2009

In this paper, we introduce and formulate the definitions of Banach operator type k and Banach operator pair on intuitionistic fuzzy metric space. Thereafter we prove some properties and theorems on intuitionistic fuzzy metric space.

• Korean Journal of Mathematics
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• v.27 no.3
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• pp.819-830
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• 2019

This paper is mainly concerned with the existence and uniqueness of fixed points of $f:X^k{\rightarrow}X$, $k{\in}{\mathbb{N}}$, where X is a quasi-partial metric space and mapping f satisfies appropriate conditions. Results are also supported with relevant examples.

• The Pure and Applied Mathematics
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• v.31 no.2
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• pp.217-233
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• 2024

In this paper we study a tripled quasi-metric with new fixed point theorems around β-implicit contractions in tripled quasi-metric spaces. We give an example on a solution of a integral equations.

• Bulletin of the Korean Mathematical Society
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• v.26 no.2
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• pp.191-201
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• 1989

In this article we are interested in characterizing when metric projection is Lipschitz continuous and determining when metric selections which are also Lipschitz continuous exist.

• ETRI Journal
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• v.38 no.6
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• pp.1114-1123
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• 2016

Multi-view video plus depth (MVD) has been widely used owing to its effectiveness in three-dimensional data representation. Using MVD, color videos with only a limited number of real viewpoints are compressed and transmitted along with captured or estimated depth videos. Because the synthesized views are generated from decoded real views, their original reference views do not exist at either the transmitter or receiver. Therefore, it is challenging to define an efficient metric to evaluate the quality of synthesized images. We propose a novel metric-the reduced-reference quality metric. First, the effects of depth distortion on the quality of synthesized images are analyzed. We then employ the high correlation between the local depth distortions and local color characteristics of the decoded depth and color images, respectively, to achieve an efficient depth quality metric for each real view. Finally, the objective quality metric of the synthesized views is obtained by combining all the depth quality metrics obtained from the decoded real views. The experimental results show that the proposed quality metric correlates very well with full reference image and video quality metrics.