On the radius of convexity and starlikeness of univalent functions

Bajpai, S. K.; Srivastava, R. S. L.

doi:10.1090/S0002-9939-1972-0294617-8

On the radius of convexity and starlikeness of univalent functions
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by S. K. Bajpai and R. S. L. Srivastava PDF

Proc. Amer. Math. Soc. 32 (1972), 153-160 Request permission

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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