On the average scale-invariant Cassinian metric

Key Points

• The analysis establishes geometric relationships within hyperbolic type metrics and the average scale-invariant cassinian metric.
• Key findings show that scale-invariant metric balls in euclidean spaces exhibit distinct local convexity properties.
• This analysis contributes to understanding the geometric nature of metrics in complex spaces, linking them closely to hyperbolic metrics.
• Insights derive from a comparative approach to the average scale-invariant cassinian metric and other geometric frameworks.