• Journal of the Chungcheong Mathematical Society
• /
• v.22 no.4
• /
• pp.699-716
• /
• 2009

We deal with a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric $L({\alpha},\;{\beta})$ = ${\beta}{\sum}_{k=0}^{r}(\frac{\alpha}{\beta})^k$ where ${\alpha}<{\beta}$. We introduced a Finsler space $F^n$ with an infinite series $({\alpha},{\beta})$-metric $L({\alpha},\;{\beta})=\frac{\beta^2}{\beta-\alpha}$ and investigated various geometrical properties at [6]. The purpose of the present paper is devoted to finding the condition for a Finsler space $F^n$ with an approximate infinite series $({\alpha},\;{\beta})$-metric above to be a Douglas space.

• Journal of the Chungcheong Mathematical Society
• /
• v.13 no.2
• /
• pp.81-86
• /
• 2001

In this paper, we present the proof of the property for interior metric space and geodesic space.

• Communications of the Korean Mathematical Society
• /
• v.18 no.3
• /
• pp.501-513
• /
• 2003

The Matsumoto metric is an ($\alpha,\;\bata$)-metric which is an exact formulation of the model of Finsler space. Lately, this metric was expressed as an infinite series form for $$\mid$\beat$\mid$\;<\;$\mid$\alpha$\mid$$ by the first author. He introduced an approximate Matsumoto metric as the ($\alpha,\;\bata$)-metric of finite series form and investigated it in [11]. The purpose of the present paper is devoted to finding the condition for a Finsler space with an approximate Matsumoto metric to be projectively flat.

• East Asian mathematical journal
• /
• v.27 no.5
• /
• pp.557-564
• /
• 2011

In 2007, Huang and Zhang [1] introduced a cone metric space with a cone metric generalizing the usual metric space by replacing the real numbers with Banach space ordered by the cone. They considered some fixed point theorems for contractive mappings in cone metric spaces. Since then, the fixed point theory for mappings in cone metric spaces has become a subject of interest in [1-6] and references therein. In this paper, we consider some fixed point theorems for generalized nonexpansive setvalued mappings under suitable conditions in sequentially compact cone metric spaces and complete cone metric spaces.

• Bulletin of the Korean Mathematical Society
• /
• v.37 no.2
• /
• pp.337-346
• /
• 2000

The geodesic equation in a two-dimensional Finsler space is given by the differential equation of the Weierstrass form. In the present paper, we express the differential equations of geodesics in a two-dimensional Finsler space with a generalized Kropina metric.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.2
• /
• pp.108-112
• /
• 2011

Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in intuitionistic fuzzy metric space.

• The Pure and Applied Mathematics
• /
• v.30 no.4
• /
• pp.407-416
• /
• 2023

In this paper, we introduce the concept of C^*-algebra-valued quasi b-metric space and prove some existence and uniqueness theorems. Furthermore, we prove the Hyers-Ulam stability results for fixed point problems via C^*-algebra-valued extended quasi b-metric space.

• The Pure and Applied Mathematics
• /
• v.27 no.2
• /
• pp.97-108
• /
• 2020

In this paper, we prove common fixed point theorems for two mappings by using simulation function on fuzzy metric spaces. We also deduce some consequences in modular metric spaces.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.3
• /
• pp.569-585
• /
• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.153-163
• /
• 2002

The present paper is devoted to studying the condition for a Finsler space with the second approximate Matsumoto metric to be a Berwald space and to be a Douglas space.