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We introduce and investigate a new subclass of the function class Σ of biunivalent functions of complex order defined in the open unit disk, which are associated with the Hohlov operator, satisfying subordinate conditions. Furthermore, we find estimates on the Taylor-Maclaurin coefficients | 2 | and | 3 | for functions in this new subclass. Several, known or new, consequences of the results are also pointed out.

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Let A denote the family of all functions that are analytic in the unit disk D := {z : |z| < 1} and satisfy f (0) = 0 = f (0) − 1 . Let S be the set of all functions f ∈ A that are univalent in D . In this paper the sharp upper bounds of |a 3 − a 2 | and |a 4 − a 3 | for the functions f (z) = z + ∑ ∞ n=2 a n z n being in several subclasses of S are presented.Mathematics subject classification (2010): 30C45.