On the Radius of Curvature for Convex Analytic Functions
1970 ◽
Vol 22
(3)
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pp. 486-491
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Keyword(s):
Definition 1.1. Let be analytic for |z| < 1. If ƒ is univalent, we say that ƒ belongs to the class S.Definition 1.2. Let ƒ ∈ S, 0 ≦ α < 1. Then ƒ belongs to the class of convex functions of order α, denoted by Kα, provided(1)and if > 0 is given, there exists Z0, |Z0| < 1, such thatLet ƒ ∈ Kα and consider the Jordan curve ϒτ = ƒ(|z| = r), 0 < r < 1. Let s(r, θ) measure the arc length along ϒτ; and let ϕ(r, θ) measure the angle (in the anti-clockwise sense) that the tangent line to ϒτ at ƒ(reiθ) makes with the positive real axis.
1964 ◽
Vol 14
(2)
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pp. 137-141
Keyword(s):
1973 ◽
Vol 15
(1)
◽
pp. 78-85
Keyword(s):
1977 ◽
Vol 29
(1)
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pp. 180-192
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Keyword(s):
2018 ◽
Vol 97
(3)
◽
pp. 435-445
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Keyword(s):
1996 ◽
Vol 76
(10)
◽
pp. 598-600
Keyword(s):
1994 ◽
Vol 32
(2)
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pp. 572-590
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1989 ◽
Vol 22
(7)
◽
pp. 767-782
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1992 ◽
Vol 15
(2)
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pp. 279-289
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Keyword(s):