沿着某个方向凸的调和单叶映射的构造

Construction of harmonic univalent mappings convex in one direction

本文给出调和单叶映射的凸组合和卷积单叶且沿着某个方向凸的若干充分条件,部分解决Dorf所提出的一个公开问题,相关结果推广和改进早期的一些结论.最后,通过三个例子验证所得到的主要结果.

We derive several sufficient conditions of the convex combinations and convolutions of harmonic univalent mappings to be univalent and convex in one direction, and partially solve an open problem posed by Dorff. The main theorems generalize and improve some earlier results. Finally, three examples are constructed to demonstrate the main results.