Initial Coefficient Bounds for Certain New Subclasses of bi-Bazilevič Functions and Exponentially bi-Convex Functions with Bounded Boundary Rotation.

The objective of the present article is to introduce new subclasses of bi-Bazilevič functions, bi-quasi-convex functions and α-exponentially bi-convex functions involving functions with bounded boundary rotation of order ν. For the above-said newly defined classes, we obtain first two initial coefficient bounds. In addition, the familiar Fekete–Szegö coefficient inequality is too found for the newly introduced subclasses of bi-univalent functions. Apart from the new findings that are obtained, it also improves the prior estimates that are presented already in the literature.