The extreme points of a class of functions with positive real part
1991 ◽
Vol 44
(2)
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pp. 253-261
Keyword(s):
Let P1 be the class of holomorphic functions on the unit disc U = {z: |z| < 1} for which f(0) = 1 and Re f > 0. Let also Pn be the corresponding class on the unit disc Un. The inequality |ak| ≤ 2 is known for the Taylor coefficients in the class P1. In this paper, it is generalised for the class Pn. If ρ = (ρ1, ρ2, …, ρn), with ρ1, ρ2, …, ρn nonegative integers whose greatest common divisor is equal to 1, we describe the form of the functions f ∈ Pn under the restriction |aρ| = 2. Under the same restriction, we give conditions for a function to be an extreme point of the class Pn.
1997 ◽
Vol 4
(4)
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pp. 449-459
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2021 ◽
Vol 66
(3)
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pp. 479-490
Keyword(s):
1970 ◽
Vol 23
(1)
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pp. 73-81
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1987 ◽
Vol 35
(3)
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pp. 471-479
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1979 ◽
Vol 31
(1)
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pp. 9-16
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Keyword(s):
1982 ◽
Vol 34
(1)
◽
pp. 1-7
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Keyword(s):
1986 ◽
Vol 41
(2)
◽
pp. 152-164
Keyword(s):
Keyword(s):