University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20190730Coefficient Estimates for Some Subclasses of Analytic and Bi-Univalent Functions Associated with Conic Domain3605710.22130/scma.2018.87581.449ENMuhamamd TahirDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.Nazar KhanDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.Qazi Zahoor AhmadDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.Bilal KhanDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.Gul Mehtab KhanDepartment of Mathematics, Abbottabad University of Science and Technology, Abbottabad, Pakistan.Journal Article20180605The 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.