Coefficient Estimates for a Subclass of Starlike Functions

In this note, we consider a subclass H 3 / 2 ( p ) of starlike functions f with f ″ ( 0 ) = p for a prescribed p ∈ [ 0 , 2 ] . Usually, in the study of univalent functions, estimates on the Taylor coefficients, Fekete–Szegö functional or Hankel determinats are given. Another coefficient problem which has attracted considerable attention is to estimate the moduli of successive coefficients | a n + 1 | − | a n | . Recently, the related functional | a n + 1 − a n | for the initial successive coefficients has been investigated for several classes of univalent functions. We continue this study and for functions f ( z ) = z + ∑ n = 2 ∞ a n z n ∈ H 3 / 2 ( p ) , we investigate upper bounds of initial coefficients and the difference of moduli of successive coefficients | a 3 − a 2 | and | a 4 − a 3 | . Estimates of the functionals | a 2 a 4 − a 3 2 | and | a 4 − a 2 a 3 | are also derived. The obtained results expand the scope of the theoretical results related with the functional | a n + 1 − a n | for various subclasses of univalent functions.