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On functions of bounded boundary rotation I

Published online by Cambridge University Press:  20 January 2009

D. A. Brannan
D. A. Brannan
Affiliation:
Department of Mathematics, Syracuse University, Syracuse, N.Y., 13210
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Let Vk denote the class of functions

which map conformally onto an image domain ƒ(U) of boundary rotation at most kπ (see (7) for the definition and basic properties of the class kπ). In this note we discuss the valency of functions in Vk, and also their Maclaurin coefficients.

In (8) it was shown that functions in Vk are close-to-convex in . Here we show that Vk is a subclass of the class K(α) of close-to-convex functions of order α (10) for , and we give an upper bound for the valency of functions in Vk for K>4.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 16 , Issue 4 , December 1969 , pp. 339 - 347
Copyright
Copyright © Edinburgh Mathematical Society 1969

References

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