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

DOI：10.3770/j.issn:2095-2651.2020.01.001

 作者 单位 龙品红 宁夏大学数学统计学院, 宁夏 银川 750021 汤获 赤峰学院数学统计学院, 内蒙古 赤峰 024000 汪文帅 宁夏大学数学统计学院, 宁夏 银川 750021

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.

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.