Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain

Abstract

The main objective of this investigation is to introduce certain new subclasses of the class $Sigma $ of bi-univalent functions by using concept of conic domain. Furthermore, we find non-sharp estimates on the first two Taylor-Maclaurin coefficients $ left vert a_{2}right vert $ and $left vert a_{3}right vert $ for functions in these new subclasses. We consider various corollaries and consequences of our main results. We also point out relevant connections to some of the earlier known developments.

Keywords

• Univalent function
• Analytic function
• Bi-univalent function
• Subordination between analytic functions
• Starlike and strongly starlike functions
• Conic domain