单位圆上调和映照的单叶半径

Univalent Radius of Harmonic Mapping in the Unit Disk

设f(z)=h(z)+g(z)=z+sum (a_nz_n) from n=2 to +∞+sum(b_nz^n)from n=1 to +∞为定义在单位圆盘U上的调和映照,满足条件sum(np) from n=2 to +∞(|an|+|bn|)≤1-|b1|,证明当0<p≤1时,f(z)在圆盘|z|<r0=1/(21-p)内单叶;当1<p≤2时,(z)在圆盘|z|<R=1/(22-p)内为凸像函数.所得结果推广了M.Jahangiri等和M.ztürk等的结论.

Let f（z）=h（z）＋g（z）=z＋sum （a_nz_n） from n=2 to ＋∞＋sum（b_nz^n）from n=1 to ＋∞ be a harmonic mapping of the unit disk U,satisfying sum（np） from n=2 to ＋∞（｜an｜＋｜bn｜）≤1-｜b1｜.In this paper we prove that： if 0〈p≤1,then f（z） is univalent in the disk ｜z｜〈r0=1 21-p;if 1〈p≤2,then f（z） is convex in the disk ｜z｜〈R0=1 22-p.These improve the corresponding results made by M.Jahangiri and M.ztürk.