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The Fekete-Szegő problem for strongly close-to-convex functions


Authors: H. R. Abdel-Gawad and D. K. Thomas
Journal: Proc. Amer. Math. Soc. 114 (1992), 345-349
MSC: Primary 30C45
DOI: https://doi.org/10.1090/S0002-9939-1992-1065939-0
MathSciNet review: 1065939
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $ K(\beta )$ denote the class of normalized analytic strongly close-to-convex functions of order $ \beta \geq 0$, defined in the unit disc $ D$ and let $ f \in K(\beta )$, with $ f(z) = z + {a_2}{z^2} + {a_3}{z^3} + \cdots $, for $ z \in D$. Sharp bounds are obtained for $ \vert{a_3} - \mu a_2^2\vert$ when $ \mu $ is real.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1992-1065939-0
Article copyright: © Copyright 1992 American Mathematical Society

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