2015/02/18 by Bappaditya Bhowmik, Bhowmik, Bappaditya, Goutam Satpati +3
Mathematics · #30C55 #30C62 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Meromorphic and Entire Functions
paper · pdf · doi:10.48550/arxiv.1502.05125
openalex publication_date 2015/02/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we consider meromorphic univalent functions f(z) in the unit disc with a simple pole at z=p∈(0,1) which have a k-quasiconformal extension to the extended complex plane \mathbb C, where 0≤ k < 1. We denote the class of such functions by Σk(p). We first prove an area theorem for functions in this class. Next, we derive a sufficient condition for meromorphic functions in the unit disc with a simple pole at z=p∈(0,1) to belong to the class Σk(p). Finally, we give a convolution property for functions in the class Σk(p).