Coefficient inequalities for a subclass of starlike functions

AbstractA function f(z) = z − ∑∞n = 2 anzn, an ⩾ 0, analytic and univalent in the unit disk, is said to be in the family T∗(a, b), a real and b ⩾ 0, if ¦(zf′f) − a¦ ⩽ b for all z in the unit disk. A complete characterization is found for T∗(a, b) when a ⩾ 1. Also, sharp coefficient bounds are determined for certain subclasses of T∗(a, b) when a < 1; however, examples are given to show that these bounds do not remain valid for the whole family