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

Larisa Gromova, Alexander Vasil'ev
1996 Annales Polonici Mathematici  
The functional |c 4 +pc 2 c 3 +qc 3 2 | is considered in the class S of all univalent holomorphic functions f (z) = z + ∞ n=2 cnz 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. 1991 Mathematics Subject Classification: Primary 30C55.
doi:10.4064/ap-63-1-7-12 fatcat:day5dm234jaf7lfjw3vxstaw74