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A variational method for univalent functions connected with antigraphy

Janina Macura (1996)

Banach Center Publications

The paper is devoted to a class of functions analytic and univalent in the unit disk that are connected with an antigraphy e i φ ω ¯ + i ρ e i φ / 2 . Variational formulas and Grunsky inequalities are derived. As an application there are given some estimations in the considered class of functions.

An extension of typically-real functions and associated orthogonal polynomials

Iwona Naraniecka, Jan Szynal, Anna Tatarczak (2011)

Annales UMCS, Mathematica

Two-parameters extension of the family of typically-real functions is studied. The definition is obtained by the Stjeltjes integral formula. The kernel function in this definition serves as a generating function for some family of orthogonal polynomials generalizing Chebyshev polynomials of the second kind. The results of this paper concern the exact region of local univalence, bounds for the radius of univalence, the coefficient problems within the considered family as well as the basic properties...

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