2023/10/03 by Swadesh Kumar Sahoo, Sahoo, Swadesh Kumar, Sheetal Wankhede +1
Mathematics · #30C45 #30E20 #31A05 #31A10 (Primary) 30C55 #44A20 (Secondary) #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Iterative Methods for Nonlinear Equations
paper · pdf · doi:10.48550/arxiv.2310.01965
openalex publication_date 2023/10/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This manuscript investigates the classical problem of determining conditions on the parameters α,β∈ ℂ for which the integral transform Cαβ[φ](z):=∫0z ((φ(ζ))/(ζ(1-ζ)β))α dζ is also univalent in the unit disk, where φ is a normalized univalent function. Additionally, whenever φ belongs to some subclasses of the class of univalent functions, the univalence features of the harmonic mappings corresponding to Cαβ[φ] and its rotations are derived. As applications to our primary findings, a few non-trivial univalent harmonic mappings are also provided. The primary tools employed in this manuscript are Becker's univalence criteria and the shear construction developed by Clunie and Sheil-Small.