Convolutions of planar harmonic strip mappings

We consider classes of harmonic univalent functions , that are shears of the analytic map with dilatation . We prove that if the convolution is locally one-to-one and sense-preserving, then is convex in the direction of the real axis.

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Bibliographic Details
Published in:Complex variables and elliptic equations 2021-11, Vol.66 (11), p.1904-1921
Main Authors: Dorff, Michael, Hamidi, Samaneh G., Jahangiri, Jay M., Yaar, Elif
Format: Article
Language:English
Subjects:
Convolutions
directional convexity
Harmonic functions
planar harmonic mappings
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Summary:We consider classes of harmonic univalent functions , that are shears of the analytic map with dilatation . We prove that if the convolution is locally one-to-one and sense-preserving, then is convex in the direction of the real axis.
ISSN:1747-6933
1747-6941
DOI:10.1080/17476933.2020.1789864