%0 Journal Article
%T Second Hankel Determinant for Certain Subclasses of Bi-starlike Functions Defined by Differential Operators
%J Sahand Communications in Mathematical Analysis
%I University of Maragheh
%Z 2322-5807
%A Orhan, Halit
%A Arikan, Hava
%A Çağlar, Murat
%D 2023
%\ 03/01/2023
%V 20
%N 2
%P 65-83
%! Second Hankel Determinant for Certain Subclasses of Bi-starlike Functions Defined by Differential Operators
%K Analytic functions
%K Univalent functions
%K Bi-univalent functions
%K Bi-starlike functions
%K Subordination between analytic functions
%K Hankel determinant
%R 10.22130/scma.2022.553738.1110
%X In 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.
%U https://scma.maragheh.ac.ir/article_701228_ae95b9e3fbc523ad146d5f3992ae7a16.pdf