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Disk-like functions

Published online by Cambridge University Press:  09 April 2009

Richard J. Libera
Richard J. Libera
Affiliation:
The University of Delaware Newark, Delaware
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The class s of functions f(z) which are regular and univalent in the open unit disk △ = {z: |z| < 1} each normalized by the conditionshas been studied intensively for over fifty years. A large and very successful portion of this work has dealt with subclasses of L characterized by some geometric property of f[Δ], the image of Δ under f(z), which is expressible in analytic terms. The class of starlike functions in L is one of these [3]; f(z) is starlike with respect to the origin if the segment [0,f(z)] is in f[Δ] for every z in Δ and this condition is equivalent to requiring that have a positive real part in Δ.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 11 , Issue 2 , May 1970 , pp. 251 - 256
Copyright
Copyright © Australian Mathematical Society 1970

References

[1]Jenkins, J. A., ‘On circularly symmetric functions’, Proc. Amer. Math. Soc., 6 (1955), 620–624.CrossRefGoogle Scholar
[2]Kryż, J. and Reade, M. O., ‘Koebe domains for certain classes of analytic functions’, J. d'Analyse Math., 18 (1967), 185–195.CrossRefGoogle Scholar
[3]Nehari, Z., Conformal Mapping, (McGraw-Hill, New York, 1952).Google Scholar
[4]Robertson, M. S., ‘Analytic functions starlike in one direction’, Amer. J. Math., 58 (1936), 465–472.CrossRefGoogle Scholar
[5]Tammi, O., ‘On certain combinations of the coefficients of schlicht functions’, Ann. Acad. Sci. Fennicae Ser. A. I. Máth.-Phys., No. 140, (1952) 13 pp.,Google Scholar