Abstract. In this paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions. Also, we find estimates of |a 2 | and |a 3 |. Some related consequences of the results are also pointed out. Mathematics Subject Classification: 30C45

In the present work, we propose to investigate the Fekete-Szegö inequalities certain classes of analytic and bi-univalent functions defined by subordination. The results in the bounds of the third coefficient which improve many known results concerning different classes of bi-univalent functions. Some interesting applications of the results presented here are also discussed.Keywords Bi-univalent functions · Ma-Minda starlike and Ma-Minda convex functions · Bi-starlike of Ma-Minda type and bi-convex of Ma-Minda type Mathematics Subject Classification 30C45

Abstract. In this paper we extend the concept of bi-univalent to the class of meromorphic functions. We propose to investigate the coefficient estimates for two classes of meromorphic bi-univalent functions. Also, we find estimates on the coefficients |b 0 | and |b 1 | for functions in these new classes. Some interesting remarks and applications of the results presented here are also discussed. 2010 Mathematics Subject Classification: 30C45.

In this sequel to the recent work (see Azizi et al., 2015), we investigate a subclass of analytic and bi-univalent functions in the open unit disk. We obtain bounds for initial coefficients, the Fekete-Szegö inequality and the second Hankel determinant inequality for functions belonging to this subclass. We also discuss some new and known special cases, which can be deduced from our results.

In this work, we obtain an upper bound estimate for the second Hankel determinant of a subclass N µ σ (λ, t) of analytic bi-univalent function class σ which is associated with Chebyshev polynomials in the open unit disk. 2010 Mathematics Subject Classification. Primary 30C45.