Best constants for metric space inversion inequalities

Abstract

For every metric space (X ) and origin ∈ X , we show the inequality I ( ) ≤ 2 ( ), where I ( ) = ( )/ ( ) ( ) is the metric space inversion semimetric, is a metric subordinate to I , and ∈ X \ { }. The constant 2 is best possible. MSC:30F45, 54E25