A1 Refereed original research article in a scientific journal
On the average scale-invariant Cassinian metric
Authors: Mohapatra, M.; Rasila, A.; Vuorinen, M.
Publication year: 2026
Journal: Analysis Mathematica
ISSN: 0133-3852
eISSN: 1588-273X
DOI: https://doi.org/10.1007/s10476-026-00146-4
Publication's open availability at the time of reporting: No Open Access
Publication channel's open availability : Partially Open Access publication channel
Web address : https://doi.org/10.1007/s10476-026-00146-4
Self-archived copy’s web address: https://arxiv.org/abs/2506.00810
Preprint address: https://arxiv.org/abs/2506.00810v1
Self-archived copy's version: Final draft
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.
Funding information in the publication:
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).
