TY - JOUR
T1 - Univalency of convolutions of harmonic mappings
AU - Boyd, Z.
AU - Dorff, M.
AU - Nowak, M.
AU - Romney, M.
AU - Wołoszkiewicz, M.
PY - 2014/5/15
Y1 - 2014/5/15
N2 - We consider the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping φ(z)=z/(1-z) with respective dilatations -xz and -yz, where |x|=|y|=1. We prove that any such convolution is univalent. Furthermore, in the case that x=y=-1, we show the resulting convolution is convex.
AB - We consider the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping φ(z)=z/(1-z) with respective dilatations -xz and -yz, where |x|=|y|=1. We prove that any such convolution is univalent. Furthermore, in the case that x=y=-1, we show the resulting convolution is convex.
KW - Convolutions
KW - Harmonic mappings
KW - Univalence
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U2 - 10.1016/j.amc.2014.01.162
DO - 10.1016/j.amc.2014.01.162
M3 - Article
AN - SCOPUS:84896529728
SN - 0096-3003
VL - 234
SP - 326
EP - 332
JO - Applied Mathematics and Computation
JF - Applied Mathematics and Computation
ER -