Abstract
The coefficient problem occupies an important place in the theory of univalent functions. It consists in the description of the set of values of the system {a2 ..... a~} in the class S of holomorphic univalent functions f(z) = z + a2z 2 + ... in the unit disk E = {zllz I i, in the disk E. This description is related to the "algebraic" part of the boundary. For the remaining set, Tammi has obtained majorant estimates. On certain parts of them, conjectures on the precise boundary have been stated, finding partial corroboration in [3]. The methods of the named works are based on the integration of the inequalities, generated by the Lowner differential equation. The set V4(~) is found in [4] by the method of extremal metrics.
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