论文标题
在$ \ Mathcal {s}^*（ψ）$的某些概括性上
On Certain Generalizations of $\mathcal{S}^*(ψ)$
论文作者
论文摘要
我们处理$ \ MATHCAL {S}^*（ψ）$的各种概括（Ma-Minda starlike功能），除了$ \ Mathcal {c}（ψ）（ψ）的多数化结果外，$ Ma-minda Convex函数的类别是： $ \ MATHCAL {C}（ψ）$和$ h $由$ f $在单位磁盘$ \ Mathbb {d}中以$ f $为多数，然后在给定的$ψ中，$，$我们得出一个常规方程，从而产生半径常数$ r_月份$ r_月份，$ r_月份，$ | h'（z）| h'（z）| \ leq leq | f'（z）$ q $ q $ q $ $ $ qu.因此，获得关联的结果$ \ Mathcal {s}^*（ψ）$等。 2. We find the largest radius $r_0$ so that the product function $g(z)h(z)/z$ belongs to a desired class for $|z|<r_0$ whenever $g\in \mathcal{S}^*(ψ_1)$ and $h\in \mathcal{S}^*(ψ_2).$ Also we obtain a condition for the functions to be in $ \ MATHCAL {s}^*（ψ）$ 3。我们获得了$ \ Mathcal {s}^*（ψ）$的修改变形定理，并具有一般的透视图。 4。对于固定的$ f \ in \ Mathcal {s}^*（ψ），$下属$ s_ {f}（ψ）：= \ {g：g \ prec f \} $也是为bohr-phenomenon和几个推测引入并研究的。
We deal with different kinds of generalizations of $\mathcal{S}^*(ψ)$, the class of Ma-Minda starlike functions, in addition to a majorization result of $\mathcal{C}(ψ),$ the class of Ma-Minda convex functions, which are enlisted as follows: 1. Let $h$ be an analytic function, $f$ be in $\mathcal{C}(ψ)$ and $h$ be majorized by $f$ in the unit disk $\mathbb{D},$ then for a given $ψ,$ we derive a general equation, which yields the radius constant $r_ψ$ such that $|h'(z)|\leq |f'(z)|$ in $|z|\leq r_ψ$. Consequently, obtain results associating $\mathcal{S}^*(ψ)$ and others. 2. We find the largest radius $r_0$ so that the product function $g(z)h(z)/z$ belongs to a desired class for $|z|<r_0$ whenever $g\in \mathcal{S}^*(ψ_1)$ and $h\in \mathcal{S}^*(ψ_2).$ Also we obtain a condition for the functions to be in $\mathcal{S}^*(ψ)$ 3. We obtain the modified distortion theorem for $\mathcal{S}^*(ψ)$ with a general perspective. 4. For a fixed $f\in \mathcal{S}^*(ψ),$ the class of subordinants $S_{f}(ψ):= \{g : g\prec f \} $ is introduced and studied for the Bohr-phenomenon and a couple of conjectures are also proposed.
