论文标题
某些非无数函数的星光度
Starlikeness of Certain Non-Univalent Functions
论文作者
论文摘要
我们考虑所有分析函数的类$ \ Mathcal {p} $定义的三类函数$ p（z）= 1+cz+\ dotsb $在具有正实际零件的开放单元磁盘上，并研究了这些类别的几个半径问题。头等舱由\ Mathcal {p} $和$ g/（Zp）\ in \ Mathcal {p} $ in \ Mathcal {p} $ in \ Mathcal {p} $组成的所有标准化分析功能$ f $，用于某些归一化的分析功能$ g $和$ p \ in \ Mathcal in \ Mathcal {p} $。第二类是通过更换$ |（f/g）-1 | <1 $ in \ Mathcal {p} $中的条件$ f/g \而定义的，而其他类则由$ f/f/f/f/f/f/f/f/in \ nathcal {p} $组成的标准化分析功能$ f $ in \ in \ in \ mathcal in \ mathcal in \ mathcal in \ mathcal in \ nathcal {p} $。我们已经确定了半径，因此这些类别的功能属于恒星函数的各种子类。这些子类包括顺序$α$，抛物线型星际型功能的恒星型功能，以及与Bernoulli的Lemniscate相关的类似Starlike功能的类别，反向轻便，正弦功能，有理功能，有氧功能，有氧运动，Lune，Lune，肾功能和修饰的Sigmoid函数。
We consider three classes of functions defined using the class $\mathcal{P}$ of all analytic functions $p(z)=1+cz+\dotsb$ on the open unit disk having positive real part and study several radius problems for these classes. The first class consists of all normalized analytic functions $f$ with $f/g\in\mathcal{P}$ and $g/(zp)\in\mathcal{P}$ for some normalized analytic function $g$ and $p\in \mathcal{P}$. The second class is defined by replacing the condition $f/g\in\mathcal{P}$ by $|(f/g)-1|<1$ while the other class consists of normalized analytic functions $f$ with $f/(zp)\in\mathcal{P}$ for some $p\in \mathcal{P}$. We have determined radii so that the functions in these classes to belong to various subclasses of starlike functions. These subclasses includes the classes of starlike functions of order $α$, parabolic starlike functions, as well as the classes of starlike functions associated with lemniscate of Bernoulli, reverse lemniscate, sine function, a rational function, cardioid, lune, nephroid and modified sigmoid function.
