2017/01/26 by Kargar, R., Ebadian, A., Sokół, J.
#30C45 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.1701.07779
Assume that Δ is the open unit disk in the complex plane and A is the class of normalized analytic functions in Δ. In this paper we introduce and study the class BS(α):=\f∈ A: ((zf'(z))/(f(z))-1)\prec (z)/(1-αz2), z∈Δ\, where 0≤α≤1 and \prec is the subordination relation. Some properties of this class like differential subordination, coefficients estimates and Fekete-Szegö inequality associated with the k-th root transform are considered.