On the Fekete-Szego Problem for Close-to-Convex Functions

On the Fekete-Szeg6 problem for close-to-convex functions II By WOLFRAM KOEPF Let C (fl), fl > 0, denote the family of normalized close-to-convex functions of order ft.For fl = 1 this is the usual set of close-to-convex functions, which had been defined by Kaplan.In a previous paper 3 we solved the Fekete-Szeg6 problem of maximizing l a 3 -2 a2l, 2 ~ 0, 1, for close-to-convex functions.The largest number 20 for which [a a -20 a2[ is maximized by the Koebe function z/(1 -z) 2 is 20 = 1/3.Now we generalize this result to C (fl), fl > 1, showing that the largest number 20 (fl) for which l a 3 -20 (fl)a2[ is maximized over C (fl) by k a with