Coefficient estimates and Fekete-Szeg\"{o} coefficient inequality for new subclasses of Bi-univalent

Document Type : Research Articles


Department of Mathematics, Faculty of Science, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran


In this paper, we investigate two new subclasses $S^*_\sigma(a, b)$ and $\nu_\sigma(a, b)$ of $\sigma$ consisting of analytic and bi-univalent functions satisfying subordinations in the open unit disk $\mathbb{U}$. We consider the Fekete-Szeg\"{o} inequalities for these new subclasses. Also, we establish estimates for the coefficient for these subclasses.