Abstract
We consider the convolution or Hadamard product of planar harmonic mappings that are the vertical shears of the canonical half-plane mapping ? ( 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.
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