一类固定系数解析函数的极值点与支撑点

Extreme points and support points of a class of analytic functions with fixed coefficient

设Q={f(z):f(z)=z-an+1zn+1-sum from k=n+2 to ∞(akzk)},这里an+1=(c(n+2))/((n+1)(n+3)),ak≥0,sum from k=n+2 to ∞((k(k+2))/(k+1)ak)≤1-c,0≤c≤1,n∈N,并且f(z)在单位圆盘Δ={z:|z|<1}内解析,得到函数族Q的极值点与支撑点.

Let Q={f(z):f(z)=z-an+1zn+1-sum from k=n+2 to ∞(akzk)},where an+1=c(n+2)(n+1)(n+3),ak≥0,an+1=(c(n+2))/((n+1)(n+3)),ak≥0,sum from k=n+2 to ∞((k(k+2))/(k+1)ak)≤1-c,0≤c≤1,n∈N and f(z)was analytic in the unit open disk,the extreme points and support points of the class Q were obtained.