University of MaraghehSahand Communications in Mathematical Analysis2322-580720220230301Second Hankel Determinant for Certain Subclasses of Bi-starlike Functions Defined by Differential Operators658370122810.22130/scma.2022.553738.1110ENHalitOrhanDepartment of Mathematics, Faculty of Science, Atatürk University, 25040, Erzurum, Turkiye.HavaArikanDepartment of Mathematics, Faculty of Science, Atatürk University, 25040, Erzurum, Turkiye.MuratÇağlarDepartment of Mathematics, Faculty of Science, Erzurum Technical University, 25100, Erzurum, Turkiye.0000-0001-8147-0343BJournal Article20220514In this paper, we obtain upper bounds of the initial Taylor-Maclaurin coefficients $\left\vert a_{2}\right\vert ,$ $\left\vert a_{3}\right\vert $ and $\left\vert a_{4}\right\vert $ and of the Fekete-Szegö functional $\left\vert a_{3}-\eta a_{2}^{2}\right\vert $ for certain subclasses of analytic and bi-starlike functions $\mathcal{S}_{\sigma }^{\ast }(\beta,\theta ,n,m)$ in the open unit disk. We have also obtained an upper bound of the functional $\left\vert a_{2}a_{4}-a_{3}^{2}\right\vert $ for the functions in the class $\mathcal{S}_{\sigma }^{\ast }(\beta ,\theta ,n,m)$. Moreover, several interesting applications of the results presented here are also discussed.https://scma.maragheh.ac.ir/article_701228_ae95b9e3fbc523ad146d5f3992ae7a16.pdf