Some external problems in the class of holomorphic univalent functions

Siejka, Henryka

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Displaying similar documents to “Some external problems in the class of holomorphic univalent functions”

Estimation of the functional a_3-αa_2^2 in the class S of holomorphic and univalent functions for α complex

Szwankowaki, Andrzej (2015-11-13T12:50:52Z)

Acta Universitatis Lodziensis. Folia Mathematica

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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 $l i m_{R e z \to - \infty} (g (w) - w) = 0$ .

Addenda to my work: "Estimation of the functional |a_3 - aα_2^2| in the class S of holomorphic and univalent functions for α complex"

Szwankowski, Andrzej (2015-12-18T19:21:18Z)

Acta Universitatis Lodziensis. Folia Mathematica

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Coefficients in some classes defined by subordination to multivalent majorants

Renata Jurasińska, Jan Stankiewicz (2003)

Annales Polonici Mathematici

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We present some results connected with estimation of the coefficients for some special class of functions holomorphic in the unit disc and defined by subordination to some multivalent functions.

Some univalent compositions of polynomials with univalent functions

Haakon Waadeland (1980)

Annales Polonici Mathematici

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Abstract. Let S denote the family of functions f, holomorphic and univalent in the open unit disk U, and normalized by f(0) = 0, f'(0) = 1.

Dynamics of inequalities in geometric function theory.

Elin, Mark, Reich, Simeon, Shoikhet, David (2001)

Journal of Inequalities and Applications [electronic only]

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A class of holomorphic functions defined by integral operator.

Bălăeţi, Camelia Mădă lina (2008)

Acta Universitatis Apulensis. Mathematics - Informatics

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Schroeder's functions

Henryka Śmiałek (1983)

Banach Center Publications

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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 $f (z) = z + \sum_{n = 2}^{\infty} c_{n} z^{n}$ 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.