Analytic, symmetric functions that omit zero

• Autorzy: Śladkowska Janina
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

analytic functions; typically real functions; symmetric functions; variational formulas

PL

funkcje analityczne; funkcje rzeczywiste; funkcje symetryczne; formuła wariancyjna

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
• Rocznik: 2004
• Tom: z. 27 [212]
• Strony: 69--81
• Opis fizyczny: Bibliogr. 2 poz.

Twórcy

autor

Śladkowska Janina

• 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.