含超几何函数的一类复阶亚纯函数族

On certain subclass of meromorphic functions of complex order involving the hypergeometric function

为研究解析函数的性质,选择对解析函数子族的探讨,作为对复杂的一般解析情况的验证.利用超几何函数和卷积定义了一类新的算子,运用该算子引进了一类复数阶亚纯函数族.利用解析函数的微分从属理论讨论了该函数族的积分表示、系数估计等相关性质,并给出了该函数族的一些判别准则,所得结果揭示了这类函数族的几何性质,推广了一些已有结论.

The studies of convolution operators and applications of differential subordination play an important role in the analytic function theory. Discussions on the subclasses of analytic functions can be used as a proof of the much more general analytic situations. This paper introduces and investigates a subclass of meromorphic functions of complex order involving an operator defined by the hypergeometric function and convolution. Such results as integral representation, coefficient estimates and sufficient conditions are proved by using the methods of differential subordination. The results presented here help to reveal some properties of this subclass of meromorphic functions and provide extensions of those given in some earlier works.