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On the radius of convexity and starlikeness of univalent functions


Authors: S. K. Bajpai and R. S. L. Srivastava
Journal: Proc. Amer. Math. Soc. 32 (1972), 153-160
MSC: Primary 30A32
MathSciNet review: 0294617
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Abstract: In this paper, the converses of the theorems of Bernardi (Trans. Amer. Math. Soc. 135 (1969), 429-446) for the subclasses of univalent functions, namely, starlike functions of order $ \beta $, convex functions of order $ \beta $ and close-to-convex functions of type $ \beta $ and order $ \lambda $ have been derived. In particular, these results are sharp and contain the theorems of Padmanabhan (J. London Math. Soc. (2) 1 (1969), 226-231) and Bernardi (Proc. Amer. Math. Soc. 24 (1970), 312-318) as special cases.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0294617-8
Keywords: Radius of convexity, convexity and starlikeness of univalent functions
Article copyright: © Copyright 1972 American Mathematical Society