基于Schwarzian导数的星形判据
Criteria for Starlikeness Using Schwarzian Derivatives
摘要：
对于复平面上开单位圆盘上的正规解析函数f，我们用导数Q_{ST}：= zf '（z）/f（z），Q_{CV}：=1+zf”（z）/f'（z）和Schwarzian导数Q_{SD}：=z^2（（f”（z）/f '（z）'-（f”（z）/f '（z））^2/2）$确定了星形的几个充分条件.这些条件是利用二阶微分从属理论中的星形容许准则得到的。
英文摘要：
For a normalised analytic function f defined on the open unit disk in the complex plane, we determine several sufficient conditions for starlikeness in terms of the quotients Q_{ST}:=zf'(z)/f(z), Q_{CV}:=1+zf"(z)/f'(z) and the Schwarzian derivative Q_{SD}:=z^2((f"(z)/f'(z))'-(f"(z)/f'(z))^2/2)$. These conditions were obtained by using the admissibility criteria of starlikeness in the theory of second order differential subordination.
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