Document Type: Research Paper

**Authors**

Department of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.

**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

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