UNIVALENCE CONDITIONS AND RADIUS PROBLEMS FOR HARMONIC DIFFERENTIAL OPERATORS

This article mainly studies univalence condition, the radius problem of fully starlike (fully convex) and uniformly starlike (uniformly convex) for the harmonic mapping differential operator under specific coefficient conditions. Firstly, several criteria for the univalence of harmonic differential operator terms are obtained, followed by the fully starlike and fully convex radius of the harmonic differential operator D[f] is an element of K2H(lambda). Next, the radius of uniformly starlike and uniformly convex of the harmonic differential operator is obtained. Finally, the radius of uniformly starlike and uniformly convex of the harmonic mapping convolution differential operator is obtained.