On the coefficient conjecture of Clunie and Sheil-Small on univalent harmonic mappings

DOI10.1007/s12044-015-0236-5zbMath1323.31002arXiv1403.5619OpenAlexW1009525498WikidataQ123131515 ScholiaQ123131515MaRDI QIDQ746352

Anbareeswaran Sairam Kaliraj, Saminathan Ponnusamy

Publication date: 16 October 2015

Published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1403.5619

zbMATH Keywords

harmonic functionscoefficient bounds

Mathematics Subject Classification ID

Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05) Coefficient problems for univalent and multivalent functions of one complex variable (30C50)

Related Items (14)

Coefficients of univalent harmonic mappings ⋮ Retracted article: ``Some remarks on univalent harmonic mappings ⋮ Sections of univalent harmonic mappings ⋮ Harmonic pre-Schwarzian and its applications ⋮ Unnamed Item ⋮ Stable classes of harmonic mappings ⋮ The spherical metric and univalent harmonic mappings ⋮ On the shears of univalent harmonic mappings ⋮ Rotations of convex harmonic univalent mappings ⋮ On the analytic part of univalent harmonic mappings ⋮ Harmonic mappings onto R-convex domains ⋮ On the coefficients of certain subclasses of harmonic univalent mappings with nonzero pole ⋮ Injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part ⋮ A GENERALISATION OF THE CLUNIE–SHEIL-SMALL THEOREM II

Cites Work

• Differential inequalities in linear- and affine-invariant families of harmonic mappings
• A proof of the Bieberbach conjecture
• Geometric properties of harmonic shears
• Curvature properties of planar harmonic mappings
• Stable geometric properties of analytic and harmonic functions
• Constants for Planar Harmonic Mappings
• Harmonic univalent functions
• On the non-vanishing of the Jacobian in certain one-to-one mappings
• On the Coefficients of Subordinate Functions
• Precise coefficient estimates for close-to-convex harmonic univalent mappings
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