Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Science, Atatürk University, 25040, Erzurum, Turkiye.

2 Department of Mathematics, Faculty of Science, Erzurum Technical University, 25100, Erzurum, Turkiye.

Abstract

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.

Keywords

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