2011/07/04 by David Kalaj, Kalaj, David, Saminathan Ponnusamy +4 · 1 citation
Mathematics · #30C45 #Analytic and geometric function theory #Complex Variables (math.CV) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical functions and polynomials #math.CV #msc:30C45
paper · pdf · doi:10.48550/arxiv.1107.0610
13 pages
arxiv created 2011/07/04 · openalex publication_date 2011/07/04 · arxiv updated 2011/07/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathcal H denote the class of all normalized complex-valued harmonic functions f=h+g in the unit disk \mathbb D, and let K=H+G denote the harmonic Koebe function. Let an,bn, An, Bn denote the Maclaurin coefficients of h,g,H,G, and \mathcal F=\f=h+g∈ \mathcal H: |an|≤ An and |bn|≤ Bn for n≥ 1. We show that the radius of univalence of the family \mathcal F is 0.112903.... We also show that this number is also the radius of the starlikeness of \mathcal F. Analogous results are proved for a subclass of the class of harmonic convex functions in \mathcal H. These results are obtained as a consequence of a new coefficient inequality for certain class of harmonic close-to-convex functions. Surprisingly, the new coefficient condition helps to improve Bloch-Landau constant for bounded harmonic mappings.