Geometric properties of a new hyperbolic type metric

Xinyu Chen, Xiaohui Zhang

We introduce a new distance function \(\tilde{S}_{G,c}\) in a metric space \((X,d)\), defined by \[ \tilde{S}_{G,c}(x,y)=\log\left(1+\frac{c\,d(x,y)}{\sqrt{1+d(x,G)}\sqrt{1+d(y,G)}…