Second Hankel Determinant for Certain Subclasses of Bi-starlike Functions Defined by Differential Operators

In this paper, we obtain  upper bounds of the initial Taylor-Maclaurin coefficients \left\vert a_{۲}\right\vert , \left\vert a_{۳}\right\vert and \left\vert a_{۴}\right\vert and of the Fekete-Szegö functional \left\vert a_{۳}-\eta a_{۲}^{۲}\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_{۲}a_{۴}-a_{۳}^{۲}\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.

کلیدواژه ها:

Analytic functions ، Univalent functions ، Bi-univalent functions ، Bi-starlike functions ، Subordination between analytic functions ، Hankel determinant