On functions of bounded boundary rotation I

Let V k denote the class of functions which map conformally onto an image domain ƒ( U ) of boundary rotation at most kπ (see ( 7 ) for the definition and basic properties of the class kπ ). In this note we discuss the valency of functions in V k , and also their Maclaurin coefficients. In ( 8 ) it was shown that functions in V k are close-to-convex in . Here we show that V k is a subclass of the class K (α) of close-to-convex functions of order α ( 10 ) for , and we give an upper bound for the valency of functions in V k for K >4.