On some results for meromorphic univalent functions having quasiconformal extension

2017/05/10 by Bappaditya Bhowmik, Bhowmik, Bappaditya, Goutam Satpati +1
Mathematics · #30C55 #30C62 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1705.03660

openalex publication_date 2017/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the class Σ(p) of univalent meromorphic functions f on \ID having simple pole at z=p∈[0,1) with residue 1. Let Σ_k(p) be the class of functions in Σ(p) which have k-quasiconformal extension to the extended complex plane \sphere %with q=(1+k)/(1-k) where 0≤ k < 1. We first give a representation formula for functions in this class and using this formula we derive an asymptotic estimate of the Laurent coefficients for the functions in the class Σ_k(p). Thereafter we give a sufficient condition for functions in Σ(p) to belong in the class Σ_k(p). Finally we obtain a sharp distortion result for functions in Σ(p) and as a consequence, we get a distortion estimate for functions in Σ_k(p).

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