On Ozaki Close-to-Convex Functions with Bounded Boundary Rotation

Abstract

In the present investigation, we introduce a new subclass of univalent functions F(u,λ) and a subclass of bi-univalent function Fo,Σ(u,λ) with bounded boundary and bounded radius rotation. Some examples of the functions belonging to the classes F(u,λ) are also derived. For these new classes, the authors derive many interesting relations between these classes and the existing familiar subclasses in the literature. Furthermore, the authors establish new coefficient estimates for these classes. Apart from the above, the first two initial coefficient bounds for the class Fo,Σ(u,λ) are established.