Criteria for Starlikeness Using Schwarzian Derivatives

2022/01/03 by Sebastian, Asha, Ravichandran, V.
#Complex Variables (math.CV) #FOS: Mathematics

paper · doi:10.48550/arxiv.2201.00497

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:=z²((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.

Related

• Some applications of differential subordination for certain starlike functions
• New criteria for starlikeness in the unit disc
• Starlikeness Using Special Functions and Subordination
• Starlikeness Associated With The Exponential Function
• Starlikeness for Certain Close-to-Star Functions