Fekete-Szeg\"{o} Functional Problems for Certain Subclasses of Bi-Univalent Functions Involving the Hohlov Operator
Received:March 24, 2019  Revised:October 09, 2019
Key Word: Fekete-Szeg\"{o} problem   analytic function   bi-univalent function   Gaussian hypergeometric function   Hohlov operator
Fund ProjectL:Supported by Science and Technology Research Project of Colleges and Universities in Ningxia (Grant No.NGY2017011), Program for Young Talents of Science and Technology in Universities of Inner Mongolia Autonomous Region (Grant No.NJYT-18-44), the Natural Science Foundation of Inner Mongolia (Grant No.2018MS01026) and the Natural Science Foundation of China (Grant Nos.11561055; 11561001; 11762016).
 Author Name Affiliation Pinhong LONG School of Mathematics and Statistics, Ningxia University, Ningxia 750021, P. R. China Huo TANG School of Mathematics and Statistics, Chifeng University, Inner Mongolia 024000, P. R. China Wenshuai WANG School of Mathematics and Statistics, Ningxia University, Ningxia 750021, P. R. China
Hits: 155
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.