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On the estimate of the fourth-order homogeneous coefficient functional for univalent functions

Larisa GromovaAlexander Vasil'ev — 1996

Annales Polonici Mathematici

The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class of all univalent holomorphic functions f ( z ) = z + n = 2 c n z n in the unit disk. For real values p and q in some regions of the (p,q)-plane the estimates of this functional are obtained by the area method for univalent functions. Some new regions are found where the Koebe function is extremal.

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