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An Inequality which Implies the correctness of the Robertson Conjecture (Milin 1971). de Branges (1985) proved this conjecture, which led to the proof of the full Bieberbach Conjecture.
See also Bieberbach Conjecture, Robertson Conjecture
References
de Branges, L. ``A Proof of the Bieberbach Conjecture.'' Acta Math. 154, 137-152, 1985.
Milin, I. M. Univalent Functions and Orthonormal Systems. Providence, RI: Amer. Math. Soc., 1977.
Stewart, I. From Here to Infinity: A Guide to Today's Mathematics.
Oxford, England: Oxford University Press, p. 165, 1996.