Abstract. Let ip : C 2 -> C be an analytic function in a domain A C C 2 , let p an analytic function in the unit disc U such that ip (p(z), zp'(z)) is univalent in U and suppose that p satisfies the first-order differential superordinationIn the case when implies q(z) -< p(z), for all p functions that satisfies the above superordination. Moreover, they found sufficient conditions so that the q function is the largest function with this property, called the best subordinant of this subordination.1991 Mathematics Subject Classification: Primary 30C80; Secondary 30C45, 30A20.

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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 a 2 and a 3 for functions in this subclass, and we obtain an estimation for the Fekete-Szegő problem for this function class.

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