卷入Hohlov 算子的双单值函数某些子类的Fekete-Szeg\"o泛函问题

Fekete-Szeg\"{o} Functional Problems for Certain Subclasses of Bi-Univalent Functions Involving the Hohlov Operator

中文关键词:  Fekete-Szeg\"o问题  解析函数  双单值函数  Gaussian 超几何函数  Hohlov算子

英文关键词:Fekete-Szeg\"{o} problem  analytic function  bi-univalent function  Gaussian hypergeometric function  Hohlov operator

中文摘要:

      本文介绍并研究了卷入Hohlov算子的双单值函数类$\sum$的新子类$\mathcal{N}^{a,b,c}_{\sum}(\mu,\lambda;\phi)$和$\mathcal{M}^{a,b,c}_{\sum}(\lambda;\phi)$与系数$a_2$和$a_3$的有界估计一样对应的Fekete-Szeg\"o泛函不等式也被得到.进而,与早期某些已知结果的因果关系和联系也将给出.

英文摘要:

      In the paper the new subclasses $\mathcal{N}^{a,b,c}_{\sum}(\mu,\lambda;\phi)$ and $\mathcal{M}^{a,b,c}_{\sum}(\lambda;\phi)$ of the function class $\sum$ of bi-univalent functions involving the Hohlov operator are introduced and investigated. Then, the corresponding Fekete-Szeg\"{o} functional inequalities as well as the bound estimates of the coefficients $a_2$ and $a_3$ are obtained. Furthermore, several consequences and connections to some of the earlier known results also are given.