Radii problems and some other properties of certain classes of analytic functions with boundary rotation

In this work, we introduce some generalized classes of convex, close-to-convex, quasi-convex and strongly convex functions f(z) in the frame of a unit disc U. Our first task is to discuss some geometric properties of a class of functions f(z) for which f(U) has a boundary rotation of at most mπ, m ≥ 2. Furthermore, we determine the smallest disc of the linear combinations of functions belonging to the classes V_m [A, B], CCV_m1m2 [A, B, C, D] and QCV_m1m2 [A, B, C, D]. Condition for univalence, covering theorem and distortion result of a more generalized strongly close-to-convex functions are also obtained. Remarkable cases and the consequences of the investigation are also highlighted in the paper.