Coefficient Estimates for a Subclass of Starlike Functions

Abstract

In this note, we consider a subclass H3/2(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 |an+1|−|an|. Recently, the related functional |an+1−an| 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∞anzn∈H3/2(p), we investigate upper bounds of initial coefficients and the difference of moduli of successive coefficients |a3−a2| and |a4−a3|. Estimates of the functionals |a2a4−a32| and |a4−a2a3| are also derived. The obtained results expand the scope of the theoretical results related with the functional |an+1−an| for various subclasses of univalent functions.

Hankel determinant for certain new classes of analytic functions associated the activation functions

“…If we represent it in the form of subordination, it can be also written as In [23] , the non-sharp bounds on third Hankel determinants for were calculated. Recently, many interesting properties on the classes of analytic functions satisfying some conditions given by the ratio of convex functions and starlike were investigated, we refer to [24] , [25] , [26] , [27] , [28] , [29] .…”