Growth, Distortion and Coefficient Bounds for Plane Harmonic Mappings Convex in One Direction

Lisbeth E. Schaubroeck
2001 Rocky Mountain Journal of Mathematics  
In this paper we examine normalized harmonic functions convex in the direction of either the real or the imaginary axis. In this setting we find bounds for |f z (z)|, |fz(z)| and |f (z)|, as well as coefficient bounds on the series expansion of functions convex in the direction of the real axis. For the functions convex in the direction of the real axis, we provide the extremal functions for |f z (z)| and |fz(z)|.
doi:10.1216/rmjm/1020171580 fatcat:tidgm2wdhfgofmaermqsgb3gqq