Quasiconformal Harmonic Mappings Related to Janowski Starlike Functions

The Generalized Janowski Starlike and Close-to-Starlike Log-Harmonic Mappings

Motivated by the success of the Janowski starlike function, we consider here closely related functions for log-harmonic mappings of the form f z zh z g z defined on the open unit disc U. The functions are in the class of the generalized Janowski starlike log-harmonic mapping, Slh A,B, α , with the functional zh z in the class of the generalized Janowski starlike functions, S∗ A,B, α . By means ...

On Janowski Starlike Functions

Harmonic Mappings Related to Starlike Function of Complex Order Α

Let SH be the class of harmonic mappings defined by SH = { f = h(z) + g(z) | h(z) = z + ∞ ∑ n=2 anz , g(z) = ∞ ∑

Convex functions and quasiconformal mappings

Continuing our investigation of quasiconformal mappings with convex potentials, we obtain a new characterization of quasiuniformly convex functions and improve our earlier results on the existence of quasiconformal mappings with prescribed sets of singularities.

Harmonic Quasiconformal Mappings of Riemannian Manifolds