Injectivity of sections of univalent harmonic mappings

DOI10.1016/j.na.2013.05.016zbMath1279.30038arXiv1506.00542OpenAlexW1980753801WikidataQ123192025 ScholiaQ123192025MaRDI QIDQ395407

Liulan Li, Saminathan Ponnusamy

Publication date: 29 January 2014

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods, Czechoslovak Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1506.00542

zbMATH Keywords

convex functionspartial sumconvexclose-to-convexstarlike and univalent harmonic mappingsclose-to-convex funtionssense-preserving harmonic functions in the disk

Mathematics Subject Classification ID

Quasiconformal mappings in (mathbb{R}^n), other generalizations (30C65) Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) (30C45) Conformal mappings of special domains (30C20) Harmonic, subharmonic, superharmonic functions in two dimensions (31A05)

Related Items (25)

On harmonic \(K\)-quasiconformal mappings associated with asymmetric vertical strips ⋮ On De la Vallée Poussin means for harmonic mappings ⋮ Radius of convexity of partial sums of functions in the close-to-convex family ⋮ Coefficients of univalent harmonic mappings ⋮ Some basic geometric properties of a subclass of harmonic mappings ⋮ Sections of univalent harmonic mappings ⋮ A new subclass of close-to-convex harmonic mappings ⋮ Injectivity of sections of univalent harmonic mappings ⋮ Close-to-convexity of a class of harmonic mappings defined by a third-orderdifferential inequality ⋮ Bohr–Rogosinski radius for a certain class of close-to-convex harmonic mappings ⋮ The sharp refined Bohr–Rogosinski inequalities for certain classes of harmonic mappings ⋮ Geometric properties of certain subclass of close-to-convex harmonic mappings ⋮ On a subclass of harmonic close-to-convex mappings ⋮ Sections of stable harmonic convex functions ⋮ Bohr phenomenon for certain subclasses of harmonic mappings ⋮ Convolutions of harmonic half-plane mappings with harmonic vertical strip mappings ⋮ Disk of convexity of sections of univalent harmonic functions ⋮ On a subclass of close-to-convex harmonic mappings ⋮ On a subclass of close-to-convex harmonic mappings ⋮ Geometric properties and sections for certain subclasses of harmonic mappings ⋮ Bohr radius for certain classes of close-to-convex harmonic mappings ⋮ On a subclass of close-to-convex harmonic mappings ⋮ Coefficient estimates and radii problems for certain classes of polyharmonic mappings ⋮ Injectivity of sections of close-to-convex harmonic mappings with functions convex in one direction as analytic part ⋮ Radius of convexity of partial sums of odd functions in the close-to-convex family

Uses Software

• Mathematica

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Coefficient characterizations and sections for some univalent functions
• Injectivity of sections of univalent harmonic mappings
• Coefficient conditions for harmonic univalent mappings and hypergeometric mappings
• Starlikeness of sections of univalent functions
• Partial sums and the radius problem for some class of conformal mappings
• A note on close-to-convex functions
• On a theorem of Szegö on univalent convex maps of the unit circle
• Harmonic univalent functions with negative coefficients
• Disk of convexity of sections of univalent harmonic functions
• On schlicht mappings to domains convex in one direction
• Radius of convexity of partial sums of functions in the close-to-convex family
• The partial sums of multivalently starlike functions
• Convolutions of slanted half-plane harmonic mappings
• Solution to an open problem on convolutions of harmonic mappings
• Convolutions of harmonic convex mappings
• Uniform close-to-convexity radius of sections of functions in the close-to-convex family
• Injectivity and Starlikeness of Sections of a Class of Univalent Functions
• Radii Problems for Sections of Convex Functions
• Convolutions of planar harmonic convex mappings
• Functions Whose Derivative has a Positive Real Part
• Extension of Szegö’s Theorem on the Sections of Univalent Functions
• On the preservation of direction-convexity and the Goodman-Saff conjecture
• Pólya-Schoenberg Conjecture for Carathéodory Functions
• Harmonic univalent functions
• Variability regions for certain families of harmonic univalent mappings
• Radii Problems for Generalized Sections of Convex Functions
• Radius of convexity of partial sums of a certain power series
• Analytic Functions Star-Like in One Direction

This page was built for publication: Injectivity of sections of univalent harmonic mappings