On harmonic Bloch-type mappings

2016/07/15 by Iason Efraimidis, J. Gaona, Efraimidis, I. +5
Mathematics · #30C25 #30C50 #30D45 #30H30 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Meromorphic and Entire Functions

paper · pdf · doi:10.48550/arxiv.1607.04626

openalex publication_date 2016/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let f be a complex-valued harmonic mapping defined in the unit disk \mathbb D. We introduce the following notion: we say that f is a Bloch-type function if its Jacobian satisfies sup_{z∈\mathbb D}(1-|z|²)√(|J_f(z)|)0 and a univalent ψ such that φ= c log ψ'.

Citations

• On the derivatives of functions analytic in the unit circle and their radii of univalence and of 𝑝-valence

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