Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6421165 | Applied Mathematics and Computation | 2014 | 7 Pages |
Abstract
We consider the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping Ï(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
Authors
Z. Boyd, M. Dorff, M. Nowak, M. Romney, M. WoÅoszkiewicz,