近于凸族中函数截面的一致近于凸半径半径
Uniform close-to-convexity radius of sections of functions in the close-to-convex family
摘要：
研究了单位圆盘$\ID$上的正规化函数$f$的解析性，并证明了正则函数类$\F$满足条件$${\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>-\frac{1}{2},\quad z\in\D. $$。最近，Ponnusamy等人在\cite{samy-hiroshi-swadesh}中证明了$1/6$是该类$\F$中每个函数的每个截面的凸性半径的一致有界。证明了$1/3$是$f\in \F$的每一节的统一的单价半径。在本文中，我们肯定地解决了这个猜想。
英文摘要：
The authors consider the class $\F$ of normalized functions $f$ analytic in the unit disk $\ID$ and satisfying the condition $${\rm Re}\left(1+\frac{zf''(z)}{f'(z)}\right)>-\frac{1}{2},\quad z\in\D. $$ Recently, Ponnusamy et al. \cite{samy-hiroshi-swadesh} have shown that $1/6$ is the uniform sharp bound for the radius of convexity of every section of each function in the class $\F$. They conjectured that $1/3$ is the uniform univalence radius of every section of $f\in \F$. In this paper, we solve this conjecture affirmatively.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
