Quasisymmetric mappings in b-metric spaces

2021 ◽  
Author(s):  
Evgeniy A. Petrov ◽  
Ruslan R. Salimov
Keyword(s):  
Metric Spaces ◽  
Quasisymmetric Mappings

Quasisymmetric mappings in b-metric spaces

2021 ◽  
Vol 18 (1) ◽  
pp. 60-70
Author(s):  
Evgeniy Petrov ◽  
Ruslan Salimov
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Quasisymmetric Mapping ◽  
Quasisymmetric Mappings

Considering quasisymmetric mappings between b-metric spaces we have found a new estimation for the ratio of diameters of two subsets which are images of two bounded subsets. This result generalizes the well-known Tukia-Vaisala inequality. The condition under which the image of a b-metric space under a quasisymmetric mapping is also a b-metric space is established. Moreover, the latter question is investigated for additive metric spaces.

scholarly journals LARGE-SCALE SUBLINEARLY LIPSCHITZ GEOMETRY OF HYPERBOLIC SPACES

2018 ◽  
Vol 19 (6) ◽  
pp. 1831-1876
Author(s):  
Gabriel Pallier
Keyword(s):  
Lie Groups ◽  
Symmetric Spaces ◽  
Large Scale ◽  
Metric Spaces ◽  
Hyperbolic Metric ◽  
Hyperbolic Spaces ◽  
Asymptotic Cones ◽  
Lipschitz Maps ◽  
Quasisymmetric Mappings

Large-scale sublinearly Lipschitz maps have been introduced by Yves Cornulier in order to precisely state his theorems about asymptotic cones of Lie groups. In particular, Sublinearly bi-Lipschitz Equivalences (SBE) are a weak variant of quasi-isometries, with the only requirement of still inducing bi-Lipschitz maps at the level of asymptotic cones. We focus here on hyperbolic metric spaces and study properties of boundary extensions of SBEs, reminiscent of quasi-Möbius (or quasisymmetric) mappings. We give a dimensional invariant of the boundary that allows to distinguish hyperbolic symmetric spaces up to SBE, answering a question of Druţu.

scholarly journals The properties of quasisymmetric mappings in metric spaces

2016 ◽  
Vol 435 (2) ◽  
pp. 1591-1606
Author(s):  
Hongjun Liu ◽  
Xiaojun Huang
Keyword(s):  
Metric Spaces ◽  
Quasisymmetric Mappings

Crystallography in two-dimensional metric spaces*

1969 ◽  
Vol 130 (1-6) ◽  
pp. 277-303 ◽  
Author(s):  
Aloysio Janner ◽  
Edgar Ascher
Keyword(s):  
Metric Spaces ◽  
Two Dimensional

Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem

2016 ◽  
Vol 2017 (1) ◽  
pp. 17-30 ◽  
Author(s):  
Muhammad Usman Ali ◽  
◽  
Tayyab Kamran ◽  
Mihai Postolache ◽  
◽  
...  
Keyword(s):  
Fixed Point ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Metric Spaces ◽  
Integral Inclusion

ON THE QUANTIFICATION OF UNIFORM PROPERTIES.PART 2

2001 ◽  
Vol 37 (1-2) ◽  
pp. 169-184
Author(s):  
B. Windels
Keyword(s):  
Metric Spaces ◽  
Uniform Spaces ◽  
Complete Metric Spaces ◽  
The Subject

In 1930 Kuratowski introduced the measure of non-compactness for complete metric spaces in order to measure the discrepancy a set may have from being compact.Since then several variants and generalizations concerning quanti .cation of topological and uniform properties have been studied.The introduction of approach uniform spaces,establishes a unifying setting which allows for a canonical quanti .cation of uniform concepts,such as completeness,which is the subject of this article.

Some Common Fixed Point Theorem in Complete Metric Space of Integral Type

2018 ◽  
Vol 6 (8) ◽  
pp. 297
Author(s):  
Jagdish C. Chaudhary ◽  
Shailesh T. Patel
Keyword(s):  
Fixed Point ◽  
Common Fixed Point ◽  
Fixed Point Theorems ◽  
Metric Spaces ◽  
Complete Metric Space ◽  
Contractive Condition ◽  
Integral Type ◽  
Complete Metric Spaces ◽  
Common Fixed Point Theorems ◽  
Common Fixed Point Theorem

In this paper, we prove some common fixed point theorems in complete metric spaces for self mapping satisfying a contractive condition of Integral  type.

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