• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2005.04a
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• pp.157-160
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• 2005

In this paper, we define precompact set in intuitionistic fuzzy metric spaces and prove that any subset of an intuitionistic fuzzy metric space is compact if and only if it is precompact and complete. Also we define topologically complete intuitionistic fuzzy metrizable spaces and prove that any $G\delta$ set in a complete intuitionistic fuzzy metric spaces is a topologically complete intuitionistic fuzzy metrizable space and vice versa.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.52 no.7
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• pp.434-441
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• 2003

This paper proposes a new quantitative and objective image quality metric which is essential to verify the performance of block-based DCT image coding. The proposed metric considers not only global distortion of coded image such as spatial frequency sensitivity and channel masking using HVS based multi-channel model, but also structural distortions caused block-based coding. The experimental results show a strong correlation between proposed metric and subjective metric.

• Journal of the Chungcheong Mathematical Society
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• v.32 no.4
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• pp.393-400
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• 2019

Pajoohesh introduced the concept of k-metric spaces and Hiltzler and Seda defined the concept of metric-like spaces. Recently, Kopperman and Pajoohesh proved a fixed point theorem in complete k-metric spaces for a Lipschitz map with bound. In this paper, we prove a fixed point theorem in complete metric-like spaces for a Lipschitz map with bound.

• The Transactions of the Korean Institute of Electrical Engineers C
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• v.52 no.7
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• pp.434-434
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• 2003

This paper proposes a new quantitative and objective image quality metric which is essential to verify the performance of block-based DCT image coding The proposed metric considers not only global distortion of coded image such as spatial frequency sensitivity and channel masking using HVS based multi-channel model, but also structural distortions caused block-based coding. The experimental results show a strong correlation between propose(B metric and subjective metric.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.387-394
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• 2020

Matthews introduced the concepts of partial metric spaces and proved the Banach fixed point theorem in complete partial metric spaces. Dukic, Kadelburg, and Radenovic proved fixed point theorems for Geraghty-type mappings in complete partial metric spaces. In this paper, we prove the fixed point theorem for some contractive mapping in a complete partial metric space.

• Kyungpook Mathematical Journal
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• v.62 no.3
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• pp.485-495
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• 2022

The aim of this paper is to characterize K-contact and Sasakian manifolds whose metrics are generalized quasi-Einstein metric. It is proven that if the metric of a K-contact manifold is generalized quasi-Einstein metric, then the manifold is of constant scalar curvature and in the case of a Sasakian manifold the metric becomes Einstein under certain restriction on the potential function. Several corollaries have been provided. Finally, we consider Sasakian 3-manifold whose metric is generalized quasi-Einstein metric.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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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.

• East Asian mathematical journal
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• v.25 no.1
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• pp.107-117
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• 2009

In this paper, we give some new definitions of D-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly compatible mappings in complete D-metric spaces. We get some improved versions of several fixed point theorems in complete D-metric spaces.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.193-203
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• 2023

In view of solution to the Hilbert fourth problem, the present study engages to investigate the projectively flat special (𝛼, 𝛽)-metric and the generalised first approximate Matsumoto (𝛼, 𝛽)-metric, where 𝛼 is a Riemannian metric and 𝛽 is a differential one-form. Further, we concluded that 𝛼 is locally Projectively flat and have 𝛽 is parallel with respect to 𝛼 for both the metrics. Also, we obtained necessary and sufficient conditions for the aforementioned metrics to be locally projectively flat.

• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.169-190
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• 2023

In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality in the definition of a metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.