论文标题
Zalcman和gentrized Zalcman猜想$ \ Mathcal {u} $
Zalcman and generalized Zalcman conjecture for the class $\mathcal{U}$
论文作者
论文摘要
函数$ f（z）= z+\ sum_ {n = 2}^{\ infty} a_n z^n $，在单位磁盘$ \ mathbb d = \ {z：| z | | <1如果是，并且只有当时，\ [\ left | \ left（\ frac {z} {f（z）} \ right）^2 -1 \ right | <1 \ quad \ quad \ quad（z \ in \ mathbb d）。 \]在本文中，我们证明了Zalcman和类$ \ Mathcal {U} $的Zalcman猜想以及猜想中的某些参数值。
Function $f(z)=z+\sum_{n=2}^{\infty} a_n z^n$, normalized, analytic and univalent in the unit disk $\mathbb D=\{z:|z|<1\}$, belongs to the class $\mathcal{U}$. if, and only if, \[ \left| \left(\frac{z}{f(z)}\right)^2 -1\right|<1 \quad\quad (z\in \mathbb D). \] In this paper, we prove the Zalcman and the generalized Zalcman conjecture for the class $\mathcal{U}$ and some values of parameters in the conjectures.
