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Radii of convexity of two classes of regular functions

Published online by Cambridge University Press:  17 April 2009

P.D. Tuan
Affiliation:
Department of Mathematics, University of Tasmania, Hobart, Tasmania 7001, Australia;
V.V. Anh
Affiliation:
Department of Mathematics, University of New England, Armidale, New South Wales 2351, Australia.
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Abstract

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This paper establishes the radii of convexity of the following two classes of regular functions,

where

.

Type
Research Article
Copyright
Copyright © Australian Mathematical Society 1980

References

[1]Carathéodory, C., Theory of functions of a complex variable, Volume two, Second English Edition (translated by Steinhardt, F.. Chelsea, New York, 1960).Google Scholar
[2]Duren, Peter, “Subordination”, Complex analysis, 2229 (Proc. Conf. University of Kentucky, 1976. Lecture Notes in Mathematics, 599. Springer-Verlag, Berlin, Heidelberg, New York, 1977).CrossRefGoogle Scholar
[3]Krzyz, Jan and Reade, Maxwell O., “The radius of univalence of certain analytic functions”, Michigan Math. J. 11 (1964), 157159.CrossRefGoogle Scholar
[4]MacGregor, Thomas H., “The radius of univalence of certain analytic functions”, Proc. Amer. Math. Soc. 14 (1963), 514520.CrossRefGoogle Scholar
[5]MacGregor, Thomas H., “The radius of univalence of certain analytic functions. II”, Proc. Amer. Math. Soc. 14 (1963), 521524.CrossRefGoogle Scholar
[6]MacGregor, Thomas H., “A class of univalent functions”, Proc. Amer. Math. Soc. 15 (1964), 311317.CrossRefGoogle Scholar
[7]Nehari, Zeev, Conformal mapping, First Edition (McGraw-Hill, New York, Toronto, London, 1952).Google Scholar
[8]Reade, Maxwell O., “On close-to-convex univalent functions”, Michigan Math. J. 3 (19551956), 5962.CrossRefGoogle Scholar
[9]Reade, Maxwell O., Ogawa, Shôtarô, and Sakaguchi, Kôchi, “The radius of convexity for a certain class of analytic functions”, J. Nara Gakugei Univ. Natur. Sci. 13 (1965), 13.Google Scholar
[10]Sakaguchi, Kôichi, “The radius of convexity for a certain class of regular functions”, J. Nara Gakugei Univ. Natur. Sci. 12 (1964), 58.Google Scholar