Construction of subclasses of univalent harmonic mappings

2012/09/01 by Sumit Nagpal, Nagpal, Sumit, V. Ravichandran +1 · 1 citation
Mathematics · #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #Differential Equations and Boundary Problems #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.1209.0075

openalex publication_date 2012/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Complex-valued harmonic functions that are univalent and sense-preserving in the open unit disk are widely studied. A new methodology is employed to construct subclasses of univalent harmonic mappings from a given subfamily of univalent analytic functions. The notion of harmonic Alexander integral operator is introduced. Also, the radius of convexity for certain families of harmonic functions is determined.

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• A Unified Study of Bohr's Inequality for analytic and harmonic mappings on the Unit Disk

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