Univalence and convexity in one direction of the convolution of harmonic mappings

DOI10.1080/17476933.2013.836188zbMath1302.31001arXiv1302.5791OpenAlexW1973066830MaRDI QIDQ5495712

Sumit Nagpal, Vravi Ravichandran

Publication date: 6 August 2014

Published in: Complex Variables and Elliptic Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1302.5791

zbMATH Keywords

convolutionconvexity in one directioncomplex-valued harmonic functions

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)

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Inequalities of harmonic univalent functions with connections of hypergeometric functions ⋮ Convolutions of harmonic right half-plane mappings ⋮ On directional convexity of harmonic mappings in the plane ⋮ Convex combinations of planar harmonic mappings realized through convolutions with half-strip mappings ⋮ Convolution properties of the harmonic Koebe function and its connection with 2-starlike mappings ⋮ Convolutions of planar harmonic strip mappings

Cites Work

• Injectivity conditions in the complex plane
• A class of bounded starlike functions
• Convolutions of harmonic convex mappings
• Convolutions of planar harmonic convex mappings
• Hadamard Products of Convex Harmonic Mappings
• On the preservation of direction-convexity and the Goodman-Saff conjecture
• Harmonic univalent functions
• Fully starlike and fully convex harmonic mappings of order α
• A subclass of close-to-convex harmonic mappings