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In the present work, we propose to investigate the Fekete–Szegö 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.

Fekete–Szegö problem for certain classes of Ma-Minda bi-univalent functions