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On the radius of convexity and starlikeness of univalent functions
1972
Proceedings of the American Mathematical Society
Preserved Fulltext
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 ß, convex functions of order ß and close-to-convex functions of type ß and order A 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. (1.2) Re(l+^il)\>ô; zeD, 0 < ß < 1.
doi:10.1090/s0002-9939-1972-0294617-8
fatcat:d3n3o2pljnbqlk4huhkkwb3dae