On the average scale-invariant Cassinian metric

: Mohapatra, M.; Rasila, A.; Vuorinen, M.

: 2026

Analysis Mathematica

: 0133-3852

: 1588-273X

DOI: https://doi.org/10.1007/s10476-026-00146-4

: https://doi.org/10.1007/s10476-026-00146-4

: https://arxiv.org/abs/2506.00810

: https://arxiv.org/abs/2506.00810v1

We establish geometric relationships between the average scale-invariant Cassinian metric and other hyperbolic type metrics. We study the local convexity properties of the scale-invariant metric balls in Euclidean once punctured spaces. In addition, we study Lipschitz-conditions with respect to these metrics.

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The research was partially supported by the Natural Science Foundation of Guangdong Province (Grant No. 2024A1515010467) and the Li Ka Shing Foundation GTIIT-STU Joint Research Grant (Grant No. 2024LKSFG06).