Fekete-Szeg\"o problem for certain classes of Ma-Minda bi-univalent functions

In the present work, we propose to investigate the Fekete-Szeg\"o inequalities certain classes of analytic and bi-univalent functions defined by subordination. The results in the bounds of the third coefficient which improve many known results concerning different classes of bi-univalent functions. Some interesting applications of the results presented here are also discussed.