- Communications Faculty of Sciences University Ankara Series A1 Mathematics and Statistics
- Volume:22
- Proof of Bieberbach`s Conjecture
Proof of Bieberbach`s Conjecture
Authors : C ULUÇAY
Pages : 0-0
Doi:10.1501/Commua1_0000000626
View : 61 | Download : 7
Publication Date : 1973-01-01
Article Type : Research Paper
Abstract :It is shown by the method of 2-dinıensional cross-section that for the class S of a- nalytic and schlicht functions the inequaiity /insert ignore into journalissuearticles values(z); = z + l-l< L a. İS always true, with equality for any n, n 2 if and only if/insert ignore into journalissuearticles values(s); is a Koebe func- tion. Survey. In this paper we prove the fam o us Bieberbach’s conjecture, i. e., for the class S of analytic and schlicht functions finsert ignore into journalissuearticles values(z); ~ z a2Z^ + a,z^ + 1, the inequality i «n I n I 2 I is ahvays true, with equality for any n, n is a Koebe function ’ 2, if and only insert ignore into journalissuearticles values(1—<>i`t2);‘ = 2 + 2ei9 2^ -|- 3e2i6 z’ •••5 9 real- Up to now, the conjecture has only been proved for re = 2, 3, 4 insert ignore into journalissuearticles values(see: [2], [3], [4], [5]);. As usual let V,n-1 be the set of pOints a = ^^3, ®n-ı); belonging to functionsKeywords : Bieberbach, Conjecture, Statistics
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