The extreme points of several classes of analytic functions

被引:2
作者
Pen, ZG [1 ]
机构
[1] Hubei Univ, Coll Math & Comp Sci, Wuhan 430062, Peoples R China
关键词
Blaschke product; extreme point;
D O I
10.1016/S0252-9602(17)30530-1
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
Let P-n(c(1),c(2),...,c(n-1)) = {p(z) : p(z) is analytic in \z\ < 1 with Rep(z) > 0 and p(z) = 1 + c(1)z + c(2)z(2) +...+ c(n-1)z(n-1) + d(n)z(n) +..., where c(1),c(2),...,c(n-1) are fixed complex constants}. Let P-R,P-n(b(1),b(2),...,b(n-1)) = {p(z) : p(z) is analytic in \z\ < 1 with Rep(z) > 0 and p(z) = 1 + b(1)z + b(2)z(2) +...+ b(n-1)z(n-1) + d(n)z(n) +..., where b(1),b(2),...,b(n-1) are fixed real constants and the coefficients of p(z) are real}. Let T-n(l(1),l(2),...,l(n-1)) = {f(z) : f(z) is analytic in \z\ < 1 and f(z) = z + l(1)z(2) + l(2)z(3) +...+ l(n-1)z(n) + d(n)z(n+1) +...; where l(1),l(2),...,l(n-1) are fixed real constants and the coefficients of f(z) are real}. It is understood that P-n(c(1),c(2),...,c(n-1)), P-R,P-n(b(1),b(2),...,b(n-1)) and T-n(l(1),l(2),...,l(n-1)) are not empty when the constants c(k)(k = 1,...,n-1), b(k)(k = 1,2,...,n-1) and l(k)(k = 1,...,n-1) satisfy certain conditions. This paper obtaines the extreme points of P-n(c(1),...,c(n-1)), P-R,P-n(b(1),...,b(n-1)) and T-n(l(1),...,l(n-1)).
引用
收藏
页码:457 / 462
页数:6
相关论文
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[2]  
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