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Analytic, symmetric functions that omit zero

Śladkowska Janina

Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka

2004

z. 27 [212]

69-81

Let Fo] (b), b is an element of R denote the class of functions of the form f{z) = b+b1z+..., analytic in the unit disk U and such that 0 [...] and let Fo(b) be the set of functions of the class Fo(b) such that f(z) €is an element of R iff z (-1,1). The functions from the class ^{b) are closely related to the typically-real functions, namely for each f is an element of Fo(b) there exist two typically-real functions T1 and T2 such that f = bT1/T2. So it is possible to treat Fo (b) as a subclass of the class[...] of all the functions of the form bT1/T2, where T1,T2 are arbitrary typically-real functions. It is easy to obtain the variational formulas in the class [...] (b) by utilizing the known formulas obtained in the class of typically-real functions [1]. Certain extremal problems in the class FoR(b) and also in the class Fo(b), for example estimation from below of the second coefficient, were solved with the aid of these formulas.

Some variational formulas in the class Kn(E) and their applications

Kir'yatskis E.

Demonstratio Mathematica

1998

Vol. 31, nr 2

265-274