Geodesic
Coefficient conditions for starlike functions
Glasgow mathematical journal, Tome 29 (1987) no. 1, pp. 141-142

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Let {ak} be a sequence of non-negative real numbers satisfying a1 = l and(1)Brannan [1] proved that the function(2)is close-to-convex univalent in the unit disc D. The exampleshows that the conclusion in Brannan's theorem is sharp in that sense that “close-to-convex” cannot be replaced by the stronger one: “starlike”. It is therefore of interest to see which additional condition can guarantee this stronger conclusion. 
Ruscheweyh, S. Coefficient conditions for starlike functions. Glasgow mathematical journal, Tome 29 (1987) no. 1, pp. 141-142. doi: 10.1017/S0017089500006753
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[1] 1.Brannan, D. A., On univalent polynomials, Glasgow Math. J., 11 (1970), 102–107 Google Scholar | DOI

[2] 2.Vietoris, L., Über das Vorzeichen gewisser trigonometrischer Summen, Sitzungsber, Oest. Akad. Wiss., 167(1958), 125–135 Google Scholar

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