Displaying similar documents to “On estimating a fifth order functional for bounded univalent functions”

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

Larisa Gromova, Alexander Vasil'ev (1996)

Annales Polonici Mathematici

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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.

Applications of the theory of differential subordination for functions with fixed initial coefficient to univalent functions

Sumit Nagpal, V. Ravichandran (2012)

Annales Polonici Mathematici

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By using the theory of first-order differential subordination for functions with fixed initial coefficient, several well-known results for subclasses of univalent functions are improved by restricting the functions to have fixed second coefficient. The influence of the second coefficient of univalent functions becomes evident in the results obtained.