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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Coefficients of functions with bounded boundary rotation


Author: James W. Noonan
Journal: Proc. Amer. Math. Soc. 29 (1971), 307-312
MSC: Primary 30.43
MathSciNet review: 0274738
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Abstract: For $ k \geqq 2$ denote by $ {V_k}$ the class of normalized functions analytic in the unit disc which have boundary rotation at most $ k\pi $. For fixed $ n \leqq (k + 6)/4$ we determine the maximum of the set of values of $ \left\vert {{a_n}} \right\vert$, where $ {a_n}$ is the nth Taylor coefficient of a function in $ {V_k}$.


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DOI: https://doi.org/10.1090/S0002-9939-1971-0274738-5
Keywords: Coefficients, bounded boundary rotation, convex functions, starlike functions
Article copyright: © Copyright 1971 American Mathematical Society