On the radius of convexity and starlikeness of univalent functions

S. K. Bajpai, R. S. L. Srivastava
1972 Proceedings of the American Mathematical Society  
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