Starlikeness of Analytic Functions with Subordinate Ratios

2021/01/05 by Rosihan M. Ali, Ali, Rosihan M., Kanika Sharma +3
Mathematics · #30C45 #30C80 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory

paper · pdf · doi:10.48550/arxiv.2101.01617

openalex publication_date 2021/01/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let h be a non-vanishing analytic function in the open unit disc with h(0)=1. Consider the class consisting of normalized analytic functions f whose ratios f(z)/g(z), g(z)/z p(z), and p(z) are each subordinate to h for some analytic functions g and p. The radius of starlikeness is obtained for this class when h is chosen to be either h(z)=√(1+z) or h(z)=e^z. Further G-radius is also obtained for each of these two classes when G is a particular widely studied subclass of starlike functions. These include G consisting of the Janowski starlike functions, and functions which are parabolic starlike.

Citations

• Starlike functions associated with a cardioid

Related

• Radius of Starlikeness for Classes of Analytic Functions
• Starlikeness of Certain Non-Univalent Functions
• Starlikeness of certain analytic functions
• Radius of starlikeness for some classes containing non-univalent functions
• Starlikeness for Certain Close-to-Star Functions