Coefficient estimates for a class of star-like functions

In this note we continue the study, initiated in [1], of the class S*(α) of functions (1.1) that are analytic and univalent in the unit disc U and satisfy the condition (1.2) S*(1) is the frequently studied class of univalent star-like functions. For each α, S*(α) is a subclass of the class K(α) of close-to-convex functions of order α introduced by Pommerenke [4]. Properties of the class S*(α) proved useful in studying the coefficient behaviour of bounded univalent functions that are analytic and map U onto a convex domain [1]. In this note we investigate the problem of determining but we are able to give only a partial solution.