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Multivalent and Meromorphic Functions of Bounded Boundary Rotation

Published online by Cambridge University Press:  20 November 2018

Ronald J. Leach
Ronald J. Leach*
Affiliation:
Howard University, Washington, D.C.
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The classVk(p). We generalize the class Vk of analytic functions of bounded boundary rotation [8] by allowing critical points in the unit disc U.

Definition. Let f(z) = aqzq + . . . (q 1) be analytic in U. Then f(z) belongs to the class Vk(p) if for r sufficiently close to 1,

and

We note that (1.1) implies that / has precisely p — 1 critical points in U.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 27 , Issue 1 , 01 February 1975 , pp. 186 - 199
Copyright
Copyright © Canadian Mathematical Society 1975

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