叶形星像函数类的系数估计与Hankel行列式
Coefficient estimates and Hankel determinant for the class of leaf shaped starlike function
- University of Kalyani（卡拉尼大学）
- Raiganj University（莱甘杰大学）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
本文研究叶形星像函数子类，利用Carathéodory函数方法获得初始Taylor系数、对数系数及多个Hankel行列式的精确界，并确定极值函数。
AI中文摘要：
本文研究了一类与归一化反正弦函数 $\varphi(z)=1+\frac{2}{\pi}\arcsin z$ 相关的Ma--Minda型星像函数子类。利用Carathéodory函数方法以及Schwarz函数的精确系数估计，我们获得了该类函数初始Taylor系数和对数系数的显式精确界。我们还推导了第二Hankel行列式 \\(H_{2,2}(f)\\) 的精确估计，以及与函数及其逆的对数系数相关的Hankel行列式 \\(H_{2,1}(F_f/2)\\) 和 \\(H_{2,1}(F_{f^{-1}}/2)\\) 的精确估计。此外，我们建立了涉及对数系数之差的精确界。所有主要结果的极值函数均被确定，证实了估计的精确性。
英文摘要：
In this paper, we study a Ma--Minda type subclass of starlike functions associated with the normalized arcsine function $φ(z)=1+\frac{2}π\arcsin z.$ Using the Carathéodory function approach together with sharp coefficient estimates for Schwarz functions, we obtain explicit sharp bounds for the initial Taylor coefficients and logarithmic coefficients of functions in this class. We also derive a sharp estimate for the second Hankel determinant \(H_{2,2}(f)\), as well as for the Hankel determinants \(H_{2,1}(F_f/2)\) and \(H_{2,1}(F_{f^{-1}}/2)\) associated with the logarithmic coefficients of a function and its inverse. In addition, we establish a sharp bound for a difference involving logarithmic coefficients. The extremal functions for all the main results are identified, confirming the sharpness of the estimates.
