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

The main purpose of this article is to make use of the Horadam polynomials hnx and the generating function Πx,z, in order to introduce three new subclasses of the bi-univalent function class σ. For functions belonging to the defined classes, we then derive coefficient inequalities and the Fekete–Szegö inequalities. Some interesting observations of the results presented here are also discussed. We also provide relevant connections of our results with those considered in earlier investigations.

Abstract. In the present work, we propose to investigate the second Hankel determinant inequalities for certain class of analytic and bi-univalent functions. Some interesting 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.

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