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ASYMPTOTIC TRACTS OF LOCALLY UNIVALENT FUNCTIONS

Published online by Cambridge University Press:  15 March 2002

KARL F. BARTH  and
PHILIP J. RIPPON
KARL F. BARTH
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, NY 13244, USAkfbarth@mailbox.syr.edu
PHILIP J. RIPPON
Affiliation:
Department of Pure Mathematics, The Open University, Walton Hall, Milton Keynes MK7 6AA p.j.rippon@open.ac.uk
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Abstract

Several results are proved, related to an old problem posed by G. R. MacLane, namely whether functions in the class [Ascr ] that are locally univalent can have arc tracts. In particular, a proof is given of an assertion of MacLane that if f ∈ [Ascr ] is locally univalent and has no arc tracts, then f′ ∈ [Ascr ].

Type
PAPERS
Information
Bulletin of the London Mathematical Society , Volume 34 , Issue 2 , March 2002 , pp. 200 - 204
Copyright
© 2002 The London Mathematical Society

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