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.