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Proceedings of the American Mathematical Society

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

 

 

On the Marx conjecture for the convex hulls of families of starlike and convex mappings


Author: David J. Hallenbeck
Journal: Proc. Amer. Math. Soc. 42 (1974), 135-139
MSC: Primary 30A32
DOI: https://doi.org/10.1090/S0002-9939-1974-0325947-0
MathSciNet review: 0325947
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Abstract: We prove a Marx conjecture for the closed convex hull of the family of functions which are starlike of order $ \alpha $ and k-fold symmetric. We obtain precise results for the functions which are starlike, starlike of order $ \tfrac{1}{2}$, and starlike with 2-fold symmetry in their power series expansions.


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DOI: https://doi.org/10.1090/S0002-9939-1974-0325947-0
Keywords: Starlike of order $ \alpha $, k-fold symmetric, convex, Marx conjecture, subordination
Article copyright: © Copyright 1974 American Mathematical Society