On the best constants associated with n-distances

Kiss, Gergely and Marichal, Jean-Luc (2020) On the best constants associated with n-distances. ACTA MATHEMATICA HUNGARICA, 161 (1). pp. 341-365. ISSN 0236-5294

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Abstract

We pursue the investigation of the concept of n-distance, ann-variable version of the classical concept of distance recently introduced and investigatedby Kiss, Marichal, and Teheux. We especially focus on the challengingproblem of computing the best constant associated with a given n-distance. Inparticular, we define and investigate the best constants related to partial simplexinequalities. We also introduce and discuss some subclasses of n-distances definedby considering some properties. Finally, we discuss an interesting link betweenthe concepts of n-distance and multidistance. © 2020, Akadémiai Kiadó, Budapest, Hungary.

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