• Bulletin of the Korean Mathematical Society
• /
• v.53 no.2
• /
• pp.399-410
• /
• 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.

• Journal of the Korean Mathematical Society
• /
• v.37 no.6
• /
• pp.885-899
• /
• 2000

We obtain generalized versions of the Fan-Browder fixed point theorem for G-convex spaces. We define the class B of better admissible multimaps on G-convex spaces and show that any closed compact map in b fro ma locally G-convex uniform space into itself has a fixed point.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
• /
• 2003.09a
• /
• pp.5.2-5
• /
• 2003

In this paper, we are to find the condition that a two-dimensional Finsler space with Matsumoto metric satisfying L(${\alpha}$,${\beta}$)=${\alpha}$$^2$/(${\alpha}$-${\beta}$) be a Landsberg space and the differential equations of geodesics.

• Journal of the Chungcheong Mathematical Society
• /
• v.12 no.1
• /
• pp.23-31
• /
• 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.

• East Asian mathematical journal
• /
• v.19 no.2
• /
• pp.261-271
• /
• 2003

We deal with two metrics of Randers type, which are characterized by the solution of certain differential equations respectively. Furthermore, we will give the condition for a Finsler space with such a metric to be a locally Minkowski space or a conformally flat space, respectively.

• Kyungpook Mathematical Journal
• /
• v.53 no.3
• /
• pp.319-332
• /
• 2013

The sequence space $m(M,{\phi})^F$ of fuzzy real numbers is introduced. Some properties of this sequence space like solidness, symmetricity, convergence-free etc. are studied. We obtain some inclusion relations involving this sequence space.

• Journal of the Korean Mathematical Society
• /
• v.51 no.6
• /
• pp.1189-1207
• /
• 2014

A partial metric, also called a nonzero self-distance, is motivated by experience from computer science. Besides a lot of properties of partial metric analogous to those of metric, fixed point theorems in partial metric spaces have been studied recently. We establish several kinds of extended fixed point theorems in ordered partial metric spaces with higher dimension under generalized notions of mixed monotone mappings.

• Communications of the Korean Mathematical Society
• /
• v.35 no.1
• /
• pp.185-199
• /
• 2020

In this paper, we introduce the definitions of s_p-convergent sequence in fuzzy metric spaces and fuzzy normed spaces. We investigate relations of convergence, s_p-convergence, s_∞-convergence and st-convergence in fuzzy metric spaces and fuzzy normed spaces. We also study s_p-convergence, s_∞-convergence and st-convergence using the sub-sequence of convergent sequence in fuzzy metric spaces and fuzzy normed spaces. Stationary fuzzy normed spaces are defined and investigated. We finally define s_p-closed sets, s_∞-closed sets and st-closed sets in fuzzy metric spaces and fuzzy normed spaces and investigate relations of them.

• Communications of the Korean Mathematical Society
• /
• v.33 no.3
• /
• pp.943-960
• /
• 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.

• The Transactions of the Korean Institute of Electrical Engineers A
• /
• v.48 no.3
• /
• pp.342-349
• /
• 1999

The metric defined on the domain deformation space better measures the similarity between bounded and continuous signals for the purpose of classification via the metric distances between signals. In this paper, a modified domain deformation theory is introduced for one-dimensional signal classification. A new metric defined on a modified domain deformation for measuring the distance between signals is employed. By introducing a newly defined metric space via the newly defined Integra-Normalizer, the assumption that domain deformation is applicable only to continuous signals is removed such that any kind of integrable signal can be classified. The metric on the modified domain deformation has an advantage over the $L^2$ metric as well as the previously introduced domain deformation does.