Abstract
LetUbe the unit disk,D⊃Uan open connected set andz0∈D. Let alsoP(z0,c,D)be the class of holomorphic functions inDfor whichf(z0)=candRef(z)>0inU. We find the extreme points of the classP(z0,c,D).
Highlights
Let U be the unit disk {z :lz] < 1}, D D U an open connected set, z0 E D and H(D) be the class of holomorphic functions in D
By P(zo, c, D) we denote the class of the functions f E H(D) for which f(zo) c and Ref(z) > 0 in U
EP {(e + z)(e z)-1 "E ( 0V D}, In this paper we find the points of the subclass EP(zo, c, D). 2
Summary
Let U be the unit disk {z :lz] < 1}, D D U an open connected set, z0 E D and H(D) be the class of holomorphic functions in D. By P(zo, c, D) we denote the class of the functions f E H(D) for which f(zo) c and Ref(z) > 0 in U. Let EP(zo,c,D) be the subclass of the extreme points of the above class for P P(0, 1, U) it has proven [1] that EP {(e + z)(e z)-1 "E ( 0V D}, In this paper we find the points of the subclass EP(zo, c, D).
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