Formulas for the Nehari Coefficients of Bounded Univalent Functions

1977 ◽  
Vol 29 (3) ◽  
pp. 587-605
Author(s):  
Duane W. De Temple ◽  
David B. Oulton
Keyword(s):  
Unit Disc ◽  
Univalent Functions ◽  
Bieberbach Conjecture ◽  
Grunsky Inequalities

The Grunsky inequalities [6] and their generalizations (e.g., [5; 14; 17]) have become an increasingly important tool for the study of the coefficients of normalized univalent functions defined on the unit disc. In particular, proofs based upon the Grunsky inequalities have now settled the Bieberbach conjecture for the fifth [15] and sixth [13] coefficients. For bounded univalent functions the situation is similar, although the Grunsky inequalities go over to those of Nehari [11].

Special Functions and the Bieberbach Conjecture

1988 ◽  
Vol 95 (8) ◽  
pp. 689 ◽  
Author(s):  
Nicholas D. Kazarinoff
Keyword(s):  
Special Functions ◽  
Bieberbach Conjecture

A proof of the Bieberbach conjecture for the fifth coefficient

1972 ◽  
Vol 45 (3) ◽  
pp. 161-193 ◽  
Author(s):  
R. Pederson ◽  
M. Schiffer
Keyword(s):  
Bieberbach Conjecture

scholarly journals Bieberbach conjecture for the eighth coefficient. II.

1973 ◽  
Vol 25 (3) ◽  
pp. 257-288
Author(s):  
Mitsuru Ozawa ◽  
Yoshihisa Kubota
Keyword(s):  
Bieberbach Conjecture

scholarly journals On the asymptotic Bieberbach conjecture

1982 ◽  
Vol 5 (3) ◽  
pp. 537-543
Author(s):  
Mauriso Alves ◽  
Armando J. P. Cavalcante
Keyword(s):  
Asymptotic Behavior ◽  
Unit Disk ◽  
Absolute Constant ◽  
Positive Semidefinite ◽  
Open Unit ◽  
Open Unit Disk ◽  
Bieberbach Conjecture ◽  
Complex Functions

The setSconsists of complex functionsf, univalent in the open unit disk, withf(0)=f'(0)-1=0. We use the asymptotic behavior of the positive semidefinite FitzGerald matrix to show that there is an absolute constantN0such that, for anyf(z)=z+?n=28anzn?Swith|a3|=2.58, we have|an|<nfor alln>N0.

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