• East Asian mathematical journal
• /
• v.17 no.2
• /
• pp.191-195
• /
• 2001

The purpose of this note is to introduce various metrics and to prove the properties of given metric spaces.

• 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.

• Korean Journal of Mathematics
• /
• v.14 no.1
• /
• pp.79-83
• /
• 2006

In this paper, we apply Zermelo's problem of navigation on Riemannian manifolds to Hermitian manifolds. Using a similar technique with which we define a Randers metric in a Finsler manifold by perturbing Riemannian metric with a vector field, we construct an $(a,b,f)$-metric in a Rizza manifold from a Hermitian metric and a given vector field.

• The Pure and Applied Mathematics
• /
• v.30 no.1
• /
• pp.1-13
• /
• 2023

In this paper, we introduce double controlled cone metric spaces via two control functions. An example of a double controlled cone metric space by two incomparable functions, which is not a controlled metric space, is given. We also provide some fixed point results involving Banach type and Kannan type contractions in the setting of double controlled cone metric spaces.

• Communications of the Korean Mathematical Society
• /
• v.38 no.4
• /
• pp.1281-1298
• /
• 2023

Let (M^2m, 𝜑, g) be a B-manifold. In this paper, we introduce a new class of metric on (M^2m, 𝜑, g), obtained by a non-conformal deformation of the metric g, called a generalized Berger-type deformed metric. First we investigate the Levi-Civita connection of this metric. Secondly we characterize the Riemannian curvature, the sectional curvature and the scalar curvature. Finally, we study the proper biharmonicity of the identity map and of a curve on M with respect to a generalized Berger-type deformed metric.

• Kyungpook Mathematical Journal
• /
• v.63 no.4
• /
• pp.611-622
• /
• 2023

In this paper, we prove that every weakly Einstein slope metric, which is conformally flat on a manifold M of dimension n ≥ 3, is either a locally Minkowski metric or a Riemannian metric. We also prove the same result for conformally flat weakly Einstein Kropina metrics.

• Honam Mathematical Journal
• /
• v.46 no.2
• /
• pp.198-208
• /
• 2024

In this paper, we find the conditions for a homogeneous Finsler space with an invariant infinite series (α, β)-metric to be of Berwald type. Also, we derive the necessary and sufficient condition for such a metric to be a Douglas metric.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.877-886
• /
• 2023

The first result of this paper is to give a revised proof of Sanatammappa et al.'s recent result in a b-metric space, under appropriate choice of constants without using the continuity of the b-metric. The second is to prove a fixed point theorem under a contraction type condition in an extended b-metric space.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.4
• /
• pp.1087-1095
• /
• 2023

In this paper, the concept of a weighted b_ν(α)-metric space is introduced as a generalization of the b_ν(s)-metric space and ν-metric space. We prove some fixed point results of the Reich-type contraction in the weighted b_ν(α)-metric space. Furthermore, we generalize Reich's theorem by extending the result to a weighted b_ν(α)-metric space.

• Bulletin of the Korean Mathematical Society
• /
• v.40 no.3
• /
• pp.457-464
• /
• 2003

Given a Riemannian manifold (M, $\alpha$) with an almost Hermitian structure f and a non-vanishing covariant vector field b, consider the generalized Randers metric $L\;=\;{\alpha}+{\beta}$, where $\beta$ is a special singular Riemannian metric defined by b and f. This metric L is called an (a, b, f)-metric. We compute the inverse and the determinant of the fundamental tensor ($g_{ij}$) of an (a, b, f)-metric. Then we determine the maximal domain D of $TM{\backslash}O$ for an (a, b, f)-manifold where a y-local Finsler structure L is defined. And then we show that any (a, b, f)-manifold is quasi-C-reducible and find a condition under which an (a, b, f)-manifold is C-reducible.