On the generalized point pair function

期刊论文
发表日期：

2026年5月16日

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Chang Xu,
Xiaohui Zhang

摘要

In this paper, we study the generalized point pair function $p_G^\alpha $ $p_{G}^{α}$ . The generalized point pair function is compared with the Cassinian metric and the hyperbolic tangent function of the distance ratio metric. Furthermore, inclusion properties of the $p_G^\alpha $ $p_{G}^{α}$ metric balls with other hyperbolic-type metric balls are investigated. The strong hyperbolicity of the metric space $(\mathbb {R}^+,\log (1+p_{\mathbb {R}^+}^4))$ $(R^{+}, log (1 + p_{R^{+}}^{4}))$ is also proved.