Yu-Can Zhu | Searcharxiv

arXiv2015

Landau's theorems for certain biharmonic mappings

Let $f(z)=h(z)+\overline{g(z)}$ be a harmonic mapping of the unit disk $U$. In this paper, the sharp coefficient estimates for bounded planar harmonic mappings are established, the sharp coefficient estimates for normalized planar harmonic mappings with $|h(z)|+|g(z)|\leq M$ are also provided. As their applications, Landau's theorems for certain biharmonic mappings are provided, which improve and refine the related results of earlier authors.

math.CV↗

arXiv2012

Biholomorphic Convex Mappings of Order alpha on the Unit Ball in Hilbert Spaces

In this paper, we first introduce the concept of biholomorphic convex mapping of order alpha on the unit ball B in a complex Hilbert space X. Next we provide some sufficient conditions that a locally biholomorphic mapping f is a biholomorphic convex mapping of order alpha and give an Alexander's theorem between the subclass of convex mappings and the subclass of starlike mappings on B in Hilbert space. We also obtain the order of starlikeness of biholomorphic convex mappings of order alpha on B in Hilbert spaces. Finally, we construct some concrete examples of biholomorphic convex mappings of order alpha on B in Hilbert spaces by means of a linear operator.

math.CV↗