Locally quasihyperbolic mappings in real Banach spaces

Caicai Hu; Caicai Hu

doi:10.3934/math.20241372

AIMS Mathematics

2024, Volume 9, Issue 10: 28295-28305. doi: 10.3934/math.20241372

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Locally quasihyperbolic mappings in real Banach spaces

Caicai Hu ^,

MOE-LCSM, School of Mathematics and Statistics, Hunan Normal University, Changsha, Hunan 410081, People's Republic of China

Received: 17 June 2024 Revised: 20 September 2024 Accepted: 23 September 2024 Published: 29 September 2024
MSC : 30C65, 30F45, 30L10

In this paper, we use locally quasihyperbolic mappings to establish a characterization for quasihyperbolic mappings in Banach spaces. More generally, we prove that locally coarsely quasihyperbolic mappings are coarsely quasihyperbolic mappings, while the converse is invalid.
- quasihyperbolic metric,
- (locally) quasihyperbolic mapping,
- (locally) coarsely quasihyperbolic mapping,
- quasisymmetric mapping
Citation: Caicai Hu. Locally quasihyperbolic mappings in real Banach spaces[J]. AIMS Mathematics, 2024, 9(10): 28295-28305. doi: 10.3934/math.20241372

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Abstract

In this paper, we use locally quasihyperbolic mappings to establish a characterization for quasihyperbolic mappings in Banach spaces. More generally, we prove that locally coarsely quasihyperbolic mappings are coarsely quasihyperbolic mappings, while the converse is invalid.

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