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A geometric criterion for decomposition and multivalence

Published online by Cambridge University Press:  24 October 2008

Y. Abu-Muhanna  and
A. Lyzzaik
Y. Abu-Muhanna
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
A. Lyzzaik
Affiliation:
Department of Mathematical Sciences, King Fahd University of Petroleum and Minerals, Dhahran, Saudi Arabia
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Abstract

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.

Information

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 103 , Issue 3 , May 1988 , pp. 487 - 495
Copyright
Copyright © Cambridge Philosophical Society 1988

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References

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