Coefficient Related Problem Studies for New Subclass of Bi-univalent Functions by $(s,t)-$Derivative Operator and Quasi-subordination
Received:July 30, 2020  Revised:January 05, 2021
Key Word: bi-univalent function   $(s,t)-$derivative   quasi-subordination   coefficient estimate   Fekete–Szeg\"{o} problem   Faber polynomial expansion.  
Fund ProjectL:
Author NameAffiliationAddress
Ao En Chifeng University 内蒙古赤峰学院数学与统计学院
Shu-Hai LI Chifeng University 内蒙古赤峰学院数学与统计学院
Huo Tang Chifeng University 内蒙古赤峰学院数学与统计学院
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      In this paper we introduce and investigate a new generalized class of bi-univalent functions defined by using $(s,t)-$derivative operator and quasi-subordination in the open unit disk. We obtain the estimates of the first two coefficients $|a_2|, |a_3|$ and general coefficient $|a_n|(n\ge4)$ by using Faber polynomial expansion for the new class and some of its subclasses. And then we get Fekete–Szeg\"{o} inequality for the newly defined classes.
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