The Quasiconvexity of Quasigeodesics in Real Normed Vector Spaces

被引：1

作者：

Huang, M. ^{[1
]}

Ponnusamy, S. ^{[2
]}

Wang, X. ^{[1
]}

机构：

[1] Hunan Normal Univ, Dept Math, Changsha 410081, Hunan, Peoples R China

[2] Indian Inst Technol, Dept Math, Madras 600036, Tamil Nadu, India

来源：

RESULTS IN MATHEMATICS | 2010年 / 57卷 / 3-4期

关键词：

Uniform domain; convex domain; quasihyperbolic geodesic; quasigeodesic; quasiconvexity; UNIFORM DOMAINS;

D O I：

10.1007/s00025-010-0025-5

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we assume that E is a real normed space of dimension at least two. The aim of this paper is to show that, for any convex domain in E, each quasigeodesic in this domain is quasiconvex in the norm metric. This result gives an affirmative answer to an open problem raised recently by Vaisala.

引用

页码：239 / 256

页数：18

共 50 条

[1] The Quasiconvexity of Quasigeodesics in Real Normed Vector Spaces
M. Huang
S. Ponnusamy
X. Wang
Results in Mathematics, 2010, 57 : 239 - 256
[2] KOROVKIN TYPE INEQUALITIES IN REAL NORMED VECTOR SPACES
George A. Anastassiou
ApproximationTheoryandItsApplications, 1986, (02) : 39 - 53
[3] κ-normed topological vector spaces
Lyudkovskii, SV
SIBERIAN MATHEMATICAL JOURNAL, 2000, 41 (01) : 141 - 154
[4] ON DIFFERENTIATION IN NORMED VECTOR SPACES
FLETT, TM
JOURNAL OF THE LONDON MATHEMATICAL SOCIETY, 1967, 42 (167P): : 523 - &
[5] Penalty-Based Data Aggregation in Real Normed Vector Spaces
Coroianu, Lucian
Gagolewski, Marek
NEW TRENDS IN AGGREGATION THEORY, 2019, 981 : 160 - 171
[6] UNIONS OF JOHN DOMAINS AND UNIFORM DOMAINS IN REAL NORMED VECTOR SPACES
Li, Yaxiang
Wang, Xiantao
ANNALES ACADEMIAE SCIENTIARUM FENNICAE-MATHEMATICA, 2010, 35 (02) : 627 - 632
[7] ON SUNS AND COSUNS IN FINITE DIMENSIONAL NORMED REAL VECTOR-SPACES
HETZELT, L
ACTA MATHEMATICA HUNGARICA, 1985, 45 (1-2) : 53 - 68
[8] Isomorphism between Spaces of Multilinear Maps and Nested Compositions over Real Normed Vector Spaces
Nakasho, Kazuhisa
Futa, Yuichi
FORMALIZED MATHEMATICS, 2022, 30 (01): : 67 - 77
[9] Incenters in real normed spaces
Tomás M.S.
Aequationes mathematicae, 2004, 67 (1-2) : 63 - 72
[10] Circumcenters in real normed spaces
Tomás, MS
BOLLETTINO DELLA UNIONE MATEMATICA ITALIANA, 2005, 8B (02): : 421 - 430

← 1 2 3 4 5 →