COEFFICIENT BOUNDS FOR NEW FAMILIES OF BAZILEVIČ AND ϕ-PSEUDO-STARLIKE BI-UNIVALENT FUNCTIONS ASSOCIATED WITH SAKAGUCHI TYPE FUNCTIONS

Abstract

. In this research paper, we introduce and study two new families Z Σ ( θ,η,ϕ,t ; α ) and Z ∗ Σ ( θ,η,ϕ,t ; β ) of normalized holomorphic and bi-univalent functions which involve the Sakaguchi type Bazilevič functions and Sakaguchi type ϕ -pseudo-starlike functions. We establish the bounds for the initial Taylor-Maclaurin coefficients | a 2 | and | a 3 | for functions in each of these new families. Further, certain several special cases and consequences for our results are also pointed.