Hostname: page-component-78c5997874-m6dg7 Total loading time: 0 Render date: 2024-11-17T19:12:00.021Z Has data issue: false hasContentIssue false
  • English
  • Français

The Schwarzian derivative and estimates of functions analytic in the unit disc

Published online by Cambridge University Press:  24 October 2008

Matts Essén  and
F. R. Keogh
Matts Essén
Affiliation:
Royal Institute of Technology, Stockholm and University of Kentucky
F. R. Keogh
Affiliation:
Royal Institute of Technology, Stockholm and University of Kentucky
Get access Rights & Permissions [Opens in a new window]

Extract

Suppose that w is analytic in the open unit disc Δ in the z-plane. The Schwarzian derivative of w is defined by

(for basic properties of {w, z} we refer to Hille ((3), p. 375)). Let denote the class of functions w which are analytic in Δ and satisfy the conditions

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 78 , Issue 3 , November 1975 , pp. 501 - 511
Copyright
Copyright © Cambridge Philosophical Society 1975

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

(1)Hartman, P. and Wintner, A.On linear, second order differential equations in the unit circle. Trans. Amer. Math. Soc. 78 (1955), 492–500.CrossRefGoogle Scholar
(2)Hille, E.Remarks on a paper by Zeev Nehari. Bull. Amer. Math. Soc. 55 (1949), 552–553.CrossRefGoogle Scholar
(3)Hille, E.Analytic function theory, vol. 2 (Ginn and Company, 1962).Google Scholar
(4)Nehari, Z.The Schwarzian derivative and schlicht functions. Bull. Amer. Math. Soc. 55 (1949), 545–551.CrossRefGoogle Scholar
(5)Nehari, Z.Some criteria of univalence. Proc. Amer. Math. Soc. 5 (1954), 700–704.CrossRefGoogle Scholar
(6)Pokornyi, V. V.On some sufficient conditions for univalence. Doklady Akademii Nauk SSSR (N.S.), 79 (1951), 743–746.Google Scholar