Research Article
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Year 1973, Volume: 22 , 0 - 0, 01.01.1973
https://doi.org/10.1501/Commua1_0000000626

Abstract

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  • Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi

Proof of Bieberbach's Conjecture

Year 1973, Volume: 22 , 0 - 0, 01.01.1973
https://doi.org/10.1501/Commua1_0000000626

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
/(z) = z + l-l< L
a.
İS always true, with equality for any n, n 2 if and only if/(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
f(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
(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 (see: [2], [3], [4], [5]).
As usual let V,n-1 be the set of pOints
a = ^^3, ®n-ı)
belonging to functions

References

  • Ankara Üniversitesi – Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics Dergisi
There are 1 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

C. Uluçay This is me

Publication Date January 1, 1973
Submission Date January 1, 1973
Published in Issue Year 1973 Volume: 22

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APA Uluçay, C. (1973). Proof of Bieberbach’s Conjecture. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 22. https://doi.org/10.1501/Commua1_0000000626
AMA Uluçay C. Proof of Bieberbach’s Conjecture. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. January 1973;22. doi:10.1501/Commua1_0000000626
Chicago Uluçay, C. “Proof of Bieberbach’s Conjecture”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 22, January (January 1973). https://doi.org/10.1501/Commua1_0000000626.
EndNote Uluçay C (January 1, 1973) Proof of Bieberbach’s Conjecture. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 22
IEEE C. Uluçay, “Proof of Bieberbach’s Conjecture”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 22, 1973, doi: 10.1501/Commua1_0000000626.
ISNAD Uluçay, C. “Proof of Bieberbach’s Conjecture”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 22 (January 1973). https://doi.org/10.1501/Commua1_0000000626.
JAMA Uluçay C. Proof of Bieberbach’s Conjecture. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1973;22. doi:10.1501/Commua1_0000000626.
MLA Uluçay, C. “Proof of Bieberbach’s Conjecture”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 22, 1973, doi:10.1501/Commua1_0000000626.
Vancouver Uluçay C. Proof of Bieberbach’s Conjecture. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 1973;22.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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