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On the best constants associated with n-distances

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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 investigated by Kiss, Marichal, and Teheux. We especially focus on the challenging problem of computing the best constant associated with a given n-distance. In particular, we define and investigate the best constants related to partial simplex inequalities. We also introduce and discuss some subclasses of n-distances defined by considering some properties. Finally, we discuss an interesting link between the concepts of n-distance and multidistance.

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Acknowledgement

The authors thank Bruno Teheux for his insights and useful comments that helped improve this paper.

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Authors and Affiliations

  1. Alfréd Rényi Institute of Mathematics, Reáltanoda u. 13-15, H-1053, Budapest, Hungary

    G. Kiss

  2. Mathematics Research Unit, University of Luxembourg, Maison du Nombre, 6, avenue de la Fonte, L-4364, Esch-sur-Alzette, Luxembourg

    J.-L. Marichal

Authors
  1. G. Kiss
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  2. J.-L. Marichal
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Corresponding author

Correspondence to J.-L. Marichal.

Additional information

G. Kiss is supported by the Hungarian National Foundation for Scientific Research, Grant No. K124749, and the Premium Postdoctoral Fellowship of Hungarian Academy of Sciences.

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Kiss, G., Marichal, JL. On the best constants associated with n-distances. Acta Math. Hungar. 161, 341–365 (2020). https://doi.org/10.1007/s10474-020-01023-8

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  • DOI: https://doi.org/10.1007/s10474-020-01023-8

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