• Communications of the Korean Mathematical Society
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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.

• Journal of the Korean Mathematical Society
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• 제62권1호
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• pp.1-31
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• 2025

In this paper, we study properties of functions on smooth metric measure space (M, g, e^-f dv). We prove that any simply connected, negatively curved smooth metric measure space with a small bound of |∇f| admits a unique f-harmonic function for a given boundary value at infinity. We also prove a sharp L²_f-decay estimate for a Schrödinger equation under certain positive spectrum. As applications, we discuss the number of ends on smooth metric measure spaces. We show that the space with finite f-volume has a finite number of ends when the Bakry-Emery Ricci tensor and the bottom of Neumann spectrum satisfy some lower bounds. We also show that the number of ends with infinite f-volume is finite when the Bakry-Émery Ricci tensor is bounded below by certain positive spectrum. Finally we study the dimension of the first L²_f-cohomology of the smooth metric measure space.

• Theoretical Mathematics and Pedagogical Mathematics
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• 제19권1호
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• pp.73-86
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• 2012

This is a survey on the volume entropy and its rigidity of various metric spaces. This survey is aimed to summarize recent results as well as remaining open questions and possible directions on this subject.

• Journal of the Chungcheong Mathematical Society
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• 제12권1호
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• pp.23-31
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• 1999

The purpose of the present paper is devoted to a study of some properties on spaces with a quartic metric from the standpoint of Finsler geometry.

• Journal of the Chungcheong Mathematical Society
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• 제5권1호
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• pp.173-183
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• 1992

In this paper, we introduce the notion of the weakly 2-convergence and strongly 2-convergence for 2-metric spaces. And we investigate its properties and prove the closedness and convexity of T(z,y, z).

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제5권4호
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• pp.322-326
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• 2005

We investigate the properties of A-transformations, P-transformations and L-transformations in metric spaces, t-norms and T-fuzzy equivalence relations.

• Bulletin of the Korean Mathematical Society
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• 제60권3호
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• pp.623-636
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• 2023

In this paper, we prove some vanishing theorems under the assumptions of weighted BiRic curvature or m-Bakry-Émery-Ricci curvature bounded from below.

• Bulletin of the Korean Mathematical Society
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• 제41권1호
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• pp.45-52
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• 2004

The theory of m-th root metric has been developed by H. Shimada [8], and applied to the biology [1] as an ecological metric. The purpose of this paper is to introduce the m-th root Finsler metrics which admit ($\alpha,\;\beta$)-types. Especially in cases of m = 3, 4, we give the condition for Finsler spaces with such metrics to be locally Minkowski spaces.

• Korean Journal of Mathematics
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• 제27권4호
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• pp.861-877
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• 2019

The aim of this paper is to extend some existing fixed point results for asymptotically regular mappings to fuzzy metric spaces. For this purpose some contractive type conditions with respect to an altering distance function are used. Some new common fixed point results have been derived for such mappings. We provide suitable examples to justify our study.

• Korean Journal of Mathematics
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• 제28권2호
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• pp.169-189
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• 2020

A common fixed point result for weakly increasing mappings satisfying generalized contractive type in ordered partial S-metric spaces are derived. Also as an application of our results we consider a couple integral equations.to guarantee the existence of a common solution.