Dependence on the Parameter of Generalized Grötzsch Ring and Generalized Hübner Functions

期刊论文
发表日期：

2024年1月23日

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Qi Bao,
Yu-Ming Chu,
Miao-Kun Wang

摘要

For $a\in (0,1/2]$ $a \in (0, 1 / 2]$ and $r\in (0,1)$ $r \in (0, 1)$ , let $\mu _{a}(r)$ $μ_{a} (r)$ and $m_{a}(r)$ $m_{a} (r)$ be the generalized Grötzsch ring function and generalized Hübner function, respectively. In this paper, the authors mainly study the dependence on the parameter a of $\mu _a(r)$ $μ_{a} (r)$ and $m_a(r)$ $m_{a} (r)$ , and present several properties of $\mu _a(r)$ $μ_{a} (r)$ and $m_a(r)$ $m_{a} (r)$ , as functions of $a\in (0,1/2]$ $a \in (0, 1 / 2]$ for arbitrarily given $r\in (0,1)$ $r \in (0, 1)$ . The obtained results improve and extend some previously well-known results.