Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

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

 

 

Radii problems for sections of convex functions


Author: Herb Silverman
Journal: Proc. Amer. Math. Soc. 104 (1988), 1191-1196
MSC: Primary 30C45; Secondary 30C50
MathSciNet review: 942638
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A classical theorem of Szegö states that the sections $ {f_n}(z) = z + \sum\nolimits_{k = 2}^n {{a_k}{z^k}} $ of a convex function $ f(z) = z + \sum\nolimits_{k = 2}^\infty {{a_k}{z^k}} $ must be convex for $ \left\vert z \right\vert < \frac{1}{4}$. We determine disks $ \left\vert z \right\vert < {r_n}$ in which $ {f_n}$ is starlike and starlike of a positve order. Our proofs rely on some properties of convolutions.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 30C45, 30C50

Retrieve articles in all journals with MSC: 30C45, 30C50


Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1988-0942638-3
Keywords: Univalent, starlike, convex, convolution
Article copyright: © Copyright 1988 American Mathematical Society