Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 42, 2017, 257-284

QUASIMÖBIUS MAPS, WEAKLY QUASIMöBIUS MAPS AND UNIFORM PERFECTNESS IN QUASI-METRIC SPACES

Xiantao Wang and Qingshan Zhou

Shantou University, Department of Mathematics
Shantou 515063, P.R. China; xtwang 'at' stu.edu.cn

Shantou University, Department of Mathematics
Shantou 515063, P.R. China; q476308142 'at' qq.com

Abstract. In this paper, first, we define the weakly quasimöbius maps in quasi-metric spaces and obtain a series of elementary properties of these maps. Then we find conditions under which a weakly quasimöbius map is quasimöbius in quasi-metric spaces. With the aid of uniform perfectness, three related results are proved, and some applications are also given.

2010 Mathematics Subject Classification: Primary 30C65, 30F45; Secondary 30C20.

Key words: Quasimöbius maps, power quasimöbius maps, quasisymmetric maps, power quasisymmetric maps, uniform perfectness, σ-density, homogenous density, quasi-metric spaces.

Reference to this article: X. Wang and Q. Zhou: Quasimöbius maps, weakly quasimöbius maps and uniform perfectness in quasi-metric spaces. Ann. Acad. Sci. Fenn. Math. 42 (2017), 257-284.

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https://doi.org/10.5186/aasfm.2017.4216