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Proceedings of the American Mathematical Society

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

 

 

On functions of bounded rotation


Author: J. W. Noonan
Journal: Proc. Amer. Math. Soc. 32 (1972), 91-101
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1972-0291434-X
MathSciNet review: 0291434
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Abstract: For fixed $ k \geqq 2$, denote by $ {V_k}$ and $ {R_k}$ the classes of functions regular in the unit disc and having boundary and radial rotation, respectively, at most $ k\pi $. The concept of order of a function is defined for both $ {V_k}$ and $ {R_k}$. For functions in these classes, the growth of integral and coefficient means is studied in terms of the order of the function. Some length-area results are also obtained.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0291434-X
Keywords: Bounded boundary rotation, bounded radial rotation, convex functions, starlike functions, integral means, length-area theorems
Article copyright: © Copyright 1972 American Mathematical Society