‖X satisfying the μ-triangle inequality of (3.2.22). The proofs are exactly similar, with the exception of the evaluation of K(f, 2 −mj) in terms of the approximation error for the proof of the first theorem: we are forced to use the μ-triangle inequality (3.5.42)‖fj‖Y≤...
A Proof of the Triangle Inequality for the Tanimoto Distance. Journal of Mathematical Chemistry, 26:263-265, 1999. 10.1023/A:1019154432472.A proof of the triangle inequality for the tanimoto distance - Lipkus - 1999Lipkus, A. H.:A proof of the triangle inequality for the Tanimoto dis- ...
9.3.3 Bounding inequality C For any real vectors β, ρ and any matrix Qt=Q>0 with appropriate dimensions, it follows that −2ρtβ⩽ρtQρ+βtQ−1β. Proof Starting from the fact that [ρ+Q−1β]tQ[ρ+Q−1β]⩾0,Q>0, one expands and arranges it to yield the desire...
A Concise Proof of the Triangle Inequality for the Jaccard Distancedoi:10.1080/07468342.2018.1526020Artur GrygorianIonut E. IacobThe College Mathematics Journal
An elementary proof of the triangle inequality for the Wasserstein metricdoi:10.1090/S0002-9939-07-09020-XPhilippe ClementWolfgang DeschAmerican Mathematical Society (AMS)
An Unusual Proof of the Triangle Inequality26D99A standard proof of triangle inequality requires using Cauchy–Schwarz inequality. The proof here bypasses such tools by instead relying on expectations.doi:10.1080/07468342.2017.1397993SawhneyMehtaab