关于Shapiro‘s的一个猜想
陈志国
【期刊名称】《数学季刊：英文版》 【年(卷),期】1994(009)002
【摘要】This problem was put forward by H.S.Shapiro on Bull,London Math.Soc.16(1984)490-517,numbered 6.88[1].The original description likes following;Let the function f(x)=z+a2xw…in Smap the unit disc onto a domain with finite area A.Then Bieberbach's inequality |a2|≤2 can be sharpened to the following;|a2|≤2-CA-1/2(*)Where C is absolute constant.What is the best value of C> Aharonov and Shapiro have shown that(*) holds for some C,and havea conjecture concerning the sharp constant C and the extremal function for(*).They also conjecture that |a2|≤2-C1l-1,where l is the length of δf(D).(H.S.Shapiro) On condition that f belongs to star-alike family in addition to the above presumptions.I have resolved this conjecture and got a precise estimates;|a2|≤2(1-π1/2A-1/2)1/2.The equation is met when f is and only is identical. 【总页数】3页(37-39)
【关键词】Shapiro‘s;猜想;显象函数;复变函数 【作者】陈志国
【作者单位】InstituteofMathematics,FudanUniversity 【正文语种】英文
关于Shapiro‘s的一个猜想
