On the Pre-Schwarzian Norm and Starlikeness of Certain Logharmonic Mappings

2025/05/20 by Sushil Pandit, Pandit, Sushil
Mathematics · #30C45 #30C55 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2505.14598

openalex publication_date 2025/05/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this note, we consider certain logharmonic mappings in the unit disk \mathbbD=\z∈ℂ:|z|<1\. Next, we obtain sharp bound of pre-Schwarzian norm of such logharmonic mappings in the unit disk. Then we discuss growth theorem for the mappings. Moreover, we discuss starlikeness of logharmonic mappings and compute sufficient coefficient condition of hereditarily starlikeness. At the end, we present some example of logharmonic hereditarily starlike function.

Citations

• On the pre-Schwarzian norm of certain Logharmonic mappings
• Pre-Schwarzian and Schwarzian norm estimates for harmonic functions with fixed analytic part
• Harmonic spirallike functions and harmonic strongly starlike functions
• Some properties of univalent log-harmonic mappings
• Uniformly locally univalent harmonic mappings associated with the pre-Schwarzian norm
• Pre-Schwarzian and Schwarzian derivatives of harmonic mappings

Related

• On the pre-Schwarzian norm of certain Logharmonic mappings
• On geometrical properties of logharmonic mappings
• On the pre-Schwarzian and Schwarzian derivatives of log-harmonic mappings
• Some properties of univalent log-harmonic mappings
• Characterizing Rotationally Typically Real Logharmonic Mappings