BI-UNIVALENT FUNCTIONS CONNECTED WITH THE MITTAG-LEFFLER-TYPE BOREL DISTRIBUTION BASED UPON THE LEGENDRE POLYNOMIALS

Abstract

In this paper, we introduce new subclasses of analytic and bi-univalent functions associated with the Mittag-Leffler-type Borel distribution by using the Legendre polynomi- als. Furthermore, we find estimates on the first two Taylor-Maclaurin coefficients |a2| and |a3| for functions in these subclasses and obtain Fekete-Szegő problem for these subclasses. We also state certain new subclasses of Σ and initial coefficient estimates and Fekete-Szegő inequalities.