On subclasses of close-to-convex functions of higher order

Abstract

The classes Tk(ρ), 0≤ρ<1, k≥2, of analytic functions, using the class Vk(ρ) of functions of bounded boundary rotation, are defined and it is shown that the functions in these classes are close-to-convex of higher order. Covering theorem, arc-length result and some radii problems are solved. We also discuss some properties of the class Vk(ρ) including distortion and coefficient results.