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Abstrakty
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.
Rocznik
Tom
Strony
69--81
Opis fizyczny
Bibliogr. 2 poz.
Twórcy
autor
- Institute of Mathematics, Silesina Technical University, Gliwice, Poland
Bibliografia
- [1] G. M. Goluzin, Geometriczeskaja teorija funkcij kompleksnogo peremennogo, Izd. "Nauka" 1966.
- [2] W. Rogosinski, Uber positive harmonische Entwicklungen und typisch-reele Potenzreihen, Math. Z., 35 (1932), 93-121.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA3-0044-0033