# Best constants for metric space inversion inequalities

Open Mathematics (2013)

- Volume: 11, Issue: 5, page 865-875
- ISSN: 2391-5455

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topStephen Buckley, and Safia Hamza. "Best constants for metric space inversion inequalities." Open Mathematics 11.5 (2013): 865-875. <http://eudml.org/doc/269794>.

@article{StephenBuckley2013,

abstract = {For every metric space (X, d) and origin o ∈ X, we show the inequality I o(x, y) ≤ 2d o(x, y), where I o(x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d o is a metric subordinate to I o, and x, y ∈ X o The constant 2 is best possible.},

author = {Stephen Buckley, Safia Hamza},

journal = {Open Mathematics},

keywords = {Metric space inversion; Best constant; metric space; inversion; isometry},

language = {eng},

number = {5},

pages = {865-875},

title = {Best constants for metric space inversion inequalities},

url = {http://eudml.org/doc/269794},

volume = {11},

year = {2013},

}

TY - JOUR

AU - Stephen Buckley

AU - Safia Hamza

TI - Best constants for metric space inversion inequalities

JO - Open Mathematics

PY - 2013

VL - 11

IS - 5

SP - 865

EP - 875

AB - For every metric space (X, d) and origin o ∈ X, we show the inequality I o(x, y) ≤ 2d o(x, y), where I o(x, y) = d(x, y)/d(x, o)d(y, o) is the metric space inversion semimetric, d o is a metric subordinate to I o, and x, y ∈ X o The constant 2 is best possible.

LA - eng

KW - Metric space inversion; Best constant; metric space; inversion; isometry

UR - http://eudml.org/doc/269794

ER -

## References

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- [5] Foertsch T., Lytchak A., Schroeder V., Nonpositive curvature and the Ptolemy inequality, Int. Math. Res. Not. IMRN, 2007, 22, #rnm100 Zbl1135.53055
- [6] Foertsch T., Schroeder V., Hyperbolicity, CAT(−1)-spaces and the Ptolemy inequality, Math. Ann., 2011, 350(2), 339–356 http://dx.doi.org/10.1007/s00208-010-0560-0 Zbl1219.53042
- [7] Herron D., Shanmugalingam N., Xie X., Uniformity from Gromov hyperbolicity, Illinois J. Math., 2008, 52(4), 1065–1109 Zbl1189.30055

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