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Note on Schiffer’s Variation in the Class of Univalent Functions in the Unit Disc

Published online by Cambridge University Press:  22 January 2016

Kikuji Matsumoto
Kikuji Matsumoto*
Affiliation:
Mathematical Institute, Nagoya University
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Let S denote the class of univalent functions f(z) in the unit disc D: | z | < 1 with the following expansion:

(1) f(z) = z + a 2 z 2 + a 3 z 3 + · · · · anzn + · ··.

We denote by fn (z) the extremal function in S which gives the maximum value of the real part of an and by Dn the image of D under w = fn (z).

Information

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 32 , June 1968 , pp. 273 - 276
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1968

References

[1] Schiffer, M.: A method of variation within the family of simple functions, Proc. London Math. Soc., 44 (1938), 432–449.CrossRefGoogle Scholar
[2] Schiffer, M.: On the coefficients of simple functions, ibid., 450–452.Google Scholar