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Proceedings of the American Mathematical Society

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

 
 

 

Coefficients of symmetric functions of bounded boundary rotation


Author: Wolfram Koepf
Journal: Proc. Amer. Math. Soc. 105 (1989), 324-329
MSC: Primary 30C50
DOI: https://doi.org/10.1090/S0002-9939-1989-0930244-7
MathSciNet review: 930244
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Abstract: The well-known inclusion relation between functions with bounded boundary rotation and close-to-convex functions of some order is extended to $ m$-fold symmetric functions. This leads solving the corresponding result for close-to-convex functions to the sharp coefficient bounds for $ m$-fold symmetric functions of bounded boundary rotation at most $ k\pi $ when $ k \geq 2m$. Moreover it shows that an $ m$-fold symmetric function of bounded boundary rotation at most $ (2m + 2)\pi $ is close-to-convex and thus univalent.


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DOI: https://doi.org/10.1090/S0002-9939-1989-0930244-7
Article copyright: © Copyright 1989 American Mathematical Society

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