2025/11/07 by Biswas, Raju, Mandal, Rajib
#30C35 #30C45 #30C62 #31A05 #Complex Variables (math.CV) #FOS: Mathematics
paper · doi:10.48550/arxiv.2511.05076
In this paper, we introduce definitions of the pre-Schwarzian and the Schwarzian derivatives for any locally univalent log-harmonic mappings defined in the unit disk \mathbbD=\z∈ℂ: |z|<1\. We explore the properties and applications of these concepts in the context of geometric function theory, and we also establish a necessary and sufficient condition for a non-vanishing log-harmonic mapping having a finite pre-Schwarzian norm. Additionally, we establish a relationship between the pre-Schwarzian norm of a non-vanishing log-harmonic mapping and that of a certain analytic function in \mathbbD.