Displaying similar documents to “Estimation of the functional a_3-αa_2^2 in the class S of holomorphic and univalent functions for α complex”

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.