The main purpose of this paper is to obtain an upper bound for the second Hankel determinant functions belonging a subclass bi-univalent in open unit disk complex plane. Furthermore, presented results work improve or generalize recent works other authors.

In this paper, two new subclasses of holomorphic and bi-univalent functions are introduced by using Balancing polynomials. Then, coefficient estmations determined for the first coefficients belonging to these classses. Finally, Fekete-Szeg¨o problem is handled in defined.

In this paper, we introduce and investigate two new subclasses of the function class Σ of bi-univalent functions. Also, we find estimates of |a2| and |a3|. Some related consequences of the results are also pointed out. Mathematics Subject Classification: 30C45

In the present investigation, we define a new subclass of meromorphic bi-univalent functions class Σ′ of complex order γ ∈ C\{0}, and obtain the estimates for the coefficients |b0| and |b1|. Further we pointed out several new or known consequences of our result.

Bounds for the second Hankel determinant of certain bi-univalent functions Halit ORHAN, Nanjundan MAGESH, Jagadeesan YAMINI Department of Mathematics Faculty of Science, Atatürk University 25240 Erzurum, Turkey. Post-Graduate and Research Department of Mathematics, Government Arts College for Men, Krishnagiri 635001, Tamilnadu, India. Department of Mathematics, Govt First Grade College Vijayana...