Article ID Journal Published Year Pages File Type
6421165 Applied Mathematics and Computation 2014 7 Pages PDF
Abstract

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.

Related Topics
Physical Sciences and Engineering Mathematics Applied Mathematics
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