Displaying similar documents to “Dynamics of inequalities in geometric function theory.”

On Some Correspondence between Holomorphic Functions in the Unit Disc and Holomorphic Functions in the Left Halfplane

Ewa Ligocka (2009)

Bulletin of the Polish Academy of Sciences. Mathematics

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We study a correspondence L between some classes of functions holomorphic in the unit disc and functions holomorphic in the left halfplane. This correspondence is such that for every f and w ∈ ℍ, exp(L(f)(w)) = f(expw). In particular, we prove that the famous class S of univalent functions on the unit disc is homeomorphic via L to the class S(ℍ) of all univalent functions g on ℍ for which g(w+2πi) = g(w) + 2πi and l i m R e z → - ∞ ( g ( w ) - w ) = 0 .

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.