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Some univalence criteria

100%

Blezu D. , Pascu N. N.

2002

tom Vol. 35, nr 1

31-34

In the first part of this paper we give a new univalence criterion for the regular functions defined in the unit disk U by means of the well known Becker's criterion. [1]. Using this criterion, in second part we can find univalence for two integral operators which improve similar results given by Y. J. Kim, E. P. Merkes and J. Pfalzgraff.

An extension of typically-real functions and associated orthogonal polynomials

60%

Naraniecka I. , Szynal J. , Tatarczak A.

nr 2

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 of obtained orthogonal polynomials.