Abstract
In this paper we introduce a new subclass of the bi-univalent functions defined in the open unit disc and connected with a q-analogue derivative. We find estimates for the first two Taylor-Maclaurin coefficients mml:semantics mml:mfenced separators="" open="|" close="|"a2 mml:mfenced mml:semantics and mml:semantics mml:mfenced separators="" open="|" close="|" a3 mml:mfenced mml:semantics for functions in this subclass, and we obtain an estimation for the Fekete-Szeg problem for this function class.