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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.

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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