论文标题
Silverman课程足够的条件和半径问题
Sufficient conditions and radius problems for the Silverman class
论文作者
论文摘要
对于$ 0 <α\ leq1 $和$λ> 0，$ let \ begin {equination} \ label {1} g_ {λ，α} = \ left \ {f \ in \ mathcal {a}：\ left | \ dfrac {1-α+αzf''（z）/f'（z）/f'（z）} {zf'（z） \ end {等式}由Tuneski和Irnak引入的Silverman类的一般形式。对于此类，我们以差异不平等的形式得出了一些足够的条件。此外，我们考虑\ begin {equation} \ label {omega}的类$ω，$ ω= \ left \ {f \ in \ Mathcal {a}：| zf'（z）-f（z）-f（z）| <\ dfrac {1} {2} {2}，\; z \ in \ in \ mathbb {d} \ right \}。 \ end {equation}对于上述两个类，我们建立了涉及$ \ Mathcal {s}^*$的其他知名子类的包容关系，并找到涉及这些类别的不同对的半径估计值。
For $0<α\leq1$ and $λ>0,$ let \begin{equation}\label{1} G_{λ,α}=\left\{f\in\mathcal{A}:\left|\dfrac{1-α+αzf''(z)/f'(z)}{zf'(z)/f(z)}-(1-α)\right|<λ, z\in\mathbb{D}\right\}, \end{equation} the general form of Silverman class introduced by Tuneski and Irnak. For this class we derive some sufficient conditions in the form of differential inequalities. Further, we consider the class $Ω,$ given by \begin{equation}\label{omega} Ω=\left\{f\in\mathcal{A}:|zf'(z)-f(z)|<\dfrac{1}{2},\;z\in\mathbb{D}\right\}. \end{equation} For the above two classes, we establish inclusion relations involving some other well known subclasses of $\mathcal{S}^*$ and find radius estimates for different pairs involving these classes.
