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Proceedings of the American Mathematical Society

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

 

 

Coefficient bounds for convex functions of bounded type


Author: K.-J. Wirths
Journal: Proc. Amer. Math. Soc. 103 (1988), 525-530
MSC: Primary 30C45; Secondary 30C25, 30C50
DOI: https://doi.org/10.1090/S0002-9939-1988-0943079-5
MathSciNet review: 943079
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Abstract: A normalized univalent function is called convex of bounded type if the curvature of the curve bounding the image domain of the unit disc lies between two fixed positive numbers. Sharp bounds for the modulus of the second and the third Taylor coefficient of such functions are derived. The proof concerning the second coefficient is based on a maximum-minimum principle for locally univalent functions.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943079-5
Keywords: Convex functions, bounded type, coefficient bounds
Article copyright: © Copyright 1988 American Mathematical Society