Advanced Search

The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class of all univalent holomorphic functions $f\left(z\right)=z+{\sum }_{n=2}^{\infty }{c}_n{z}^n$ 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.