English

Criteria for Starlikeness Using Schwarzian Derivatives

Complex Variables 2022-01-04 v1

Abstract

For a normalised analytic function f defined on the open unit disk in the complex plane, we determine several sufficient conditions for starlikeness in terms of the quotients Q_{ST}:=zf'(z)/f(z), Q_{CV}:=1+zf"(z)/f'(z) and the Schwarzian derivative Q_{SD}:=z^2((f"(z)/f'(z))'-(f"(z)/f'(z))^2/2)$. These conditions were obtained by using the admissibility criteria of starlikeness in the theory of second order differential subordination.

Keywords

Cite

@article{arxiv.2201.00497,
  title  = {Criteria for Starlikeness Using Schwarzian Derivatives},
  author = {Asha Sebastian and V. Ravichandran},
  journal= {arXiv preprint arXiv:2201.00497},
  year   = {2022}
}