Volume 35 • Number 3 • 2012   • Use of Theory of Conformal Mappings in Harmonic Univalent Mappings with Directional Convexity Om P. Ahuja Abstract. In this paper we use shear construction to generate certain subclasses of harmonic univalent mappings with directional convexity because it allows us to study such functions by examining their related conformal univalent mappings. In this setting we find growth, distortion, and coefficient bounds for harmonic univalent mappings that are convex in both the directions of real axis and imaginary axis. 2010 Mathematics Subject Classification: Primary: 31A05; Secondary: 30C45, 30C55. Full text: PDF