Coefficient estimates for a new subclass of bi-univalent functions defined by convolution

In this paper we introduce general subclasses of bi-univalent functions by using convolution. Bounds for the first two coefficients and for bi-univalent functions in these classes are obtained. The obtained results generalize the results which are given in [Murugusundaramoorthy, G., Magesh, M., Prameela, V., Coefficient bounds for certain subclasses of bi-univalent function, Abstr. Appl. Anal., (2013), Art. ID 573017, 3 pp.]
and [Brannan, D. A. and Taha, T. S., On some classes of bi-univalent functions, Studia Univ. Babeş  Bolyai Math., 31 (1986), No. 2, 70–77].