调和单叶函数族的一些结果

Some Results for a Family of Harmonic Univalent Functions

中文关键词:  极值点  增长定理  调和函数  修正哈达玛乘积  Ruscheweyh导数

英文关键词:extreme points  growth theorem  harmonic functions  modified-Hadamard product  Ruscheweyh derivatives

中文摘要:

      借用著名的Ruscheweyh导数,引入了一类单叶保向调和函数族. 通过建立极值理论,得到了关联该族的最优系数边界、最优增长定理和最优偏差定理. 同时,给出了该族与先前已有调和函数族之间的转换半径. 最后,讨论了基于该族的修正哈达玛乘积结果.

英文摘要:

      In this paper, we introduce a class of the univalent sense-preserving harmonic functions associated with Ruscheweyh derivatives. By establishing the extremal theory, we obtain the sharp coefficients bounds, sharp growth theorems and sharp distortion theorems for the class. The radius equation between this class and a known class of harmonic functions is given. Also, we investigate the results of modified-Hadamard product for this class.