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On Local Maximality for the Coefficient a6

Published online by Cambridge University Press:  22 January 2016

James A. Jenkins  and
Mitsuru Ozawa
James A. Jenkins
Affiliation:
Washington University, St. Louis and Tokyo Institute of Technology, Tokyo
Mitsuru Ozawa
Affiliation:
Washington University, St. Louis and Tokyo Institute of Technology, Tokyo
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Recently a number of authors have studied the application of Grunsky’s coefficient inequalities to the study of the Bieberbach conjecture for the class of normalized regular univalent functions f(z) in the unit circle |z|< 1

Charzynski and Schiffer [2] applied this result to give an elementary proof of the inequality | a4 | Ȧ 4. One of the present authors [8] proved that if a2 is real non-negative then A natural first step in the study of the inequality for a coefficient is to prove local maximality for a2 near to 2.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 30 , August 1967 , pp. 71 - 78
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1966

References

[1] Bombieri, E., Sul problema di Bieberbach per le funzioni univalenti. Rend. Lincei 35 (1963), 469–471.Google Scholar
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[6] Jenkins, J.A., On certain coefficients of univalent functions. Analytic functions. Princeton Univ. Press (1960), 159–194.Google Scholar
[7] Jenkins, J.A., Some area theorems and a special coefficient theorem. Illinois Journ. Math. 8 (1964), 80–99.Google Scholar
[8] Ozawa, M., On the sixth coefficient of univalent function. Kōdai Math. Sem. Rep. 17 (1965), 1–9.Google Scholar