a b s t r a c tIn this paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disc. Furthermore, we find estimates on the coefficients |a 2 | and |a 3 | for functions in these new subclasses.

In this paper, we introduce two new subclasses of the function class Σ of bi-univalent functions defined in the open unit disk. Furthermore, we find estimates on the coefficients |a2| and |a3| for functions in these new subclasses.

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Abstract. We consider the class of analytic functions B(α) to investigate some properties for this class. The angular estimates of functions in the class B(α) are obtained. Finally, we derive some interesting conditions for the class of strongly starlike and strongly convex of order α in the open unit disk.