CONSTRUCTION OF UNIVALENT HARMONIC MAPPINGS AND THEIR CONVOLUTIONS.

In this article, we make use of convex analytic functions Ha(z) = [1/(1 - a)] log[(1 - az)/(1 - z)], a - ℝ, |a| ≤ 1, a ≠ 1 and starlike analytic functions Lb(z) = z/[(1 - bz)(1 - z)], b - ℝ, |b| ≤ 1, to construct univalent harmonic functions by means of a transformation on some normalized univalent analytic functions. Besides exploring mapping properties of harmonic functions so constructed, we establish sufficient conditions for their harmonic convolutions or Hadamard products to be locally univalent and sense preserving, univalent and convex in some direction. [ABSTRACT FROM AUTHOR]