Radius problems associated with pre-Schwarzian and Schwarzian derivatives

2012/03/18 by Saminathan Ponnusamy, S. Ponnusamy, Swadesh Kumar Sahoo +6 · 1 citation
Mathematics · #30C45 (Primary) 30C55 #33C05 (Secondary) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CV #msc:30C45 #msc:30C55 #msc:33C05

paper · pdf · doi:10.48550/arxiv.1203.3918

8 pages, submitted to a journal

arxiv created 2012/03/18 · openalex publication_date 2012/03/18 · arxiv updated 2012/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Some of important univalence criteria for a non-constant meromorphic function f(z) on the unit disk \ID involve its pre-Schwarzian or Schwarzian derivative. We consider an appropriate norm for the pre-Schwarzian derivative, and discuss the problem of finding the largest possible r∈ (0,1) for which the pre-Schwarzian norm of the dilation r^-1f(rz) is not greater than a prescribed number for normalized univalent functions f(z) in the unit disk. Similar results concerning the Schwarzian derivative are also obtained

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