A geometric criterion for decomposition and multivalence

We give a quite general geometric criterion for a function analytic in the unit disc to be a polynomial of a univalent function, and hence a criterion for multivalence. We believe that this is the essence why multivalent close-to-convex functions enjoy the latter decomposition property. As another a...

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Bibliographic Details
Published in:Mathematical proceedings of the Cambridge Philosophical Society 1988-05, Vol.103 (3), p.487-495
Main Authors: Abu-Muhanna, Y., Lyzzaik, A.
Format: Article
Language:English
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Summary:We give a quite general geometric criterion for a function analytic in the unit disc to be a polynomial of a univalent function, and hence a criterion for multivalence. We believe that this is the essence why multivalent close-to-convex functions enjoy the latter decomposition property. As another application, we study, as suggested by T. Sheil-Small ‘9’, the geometry of classes of analytic functions which arise from his recent investigation of multivalent harmonic mappings.
ISSN:0305-0041
1469-8064
DOI:10.1017/S0305004100065099