Communications of the
Korean Mathematical Society CKMS

In the present paper, we introduce the subclasses $mathfrak{B}_{1Sigma}(mu)$, $mathrm{B}_{1Sigma}(mu,gamma)$ and $mathit{U}_{Sigma}(mu,gamma)$ of bi-univalent Bazileviv{c} functions which are defined in the open unit disk $mathbb{D}$. Further, we obtain sharp estimates on initial coefficients $a_2$, $a_3$, $a_4$ and also sharp estimate on the Fekete-Szeg"{o} functional $a_3-k{a}_{2}^{2}$ for the functions belong to these subclasses.

Keywords: Analytic function, univalent function, bi-univalent function, star-like function, Bazileviv{c} function

MSC numbers: Primary 30C45, 30C50