On coefficients' estimates of concave univalent functions

• Autorzy: Zaprawa P.
• Języki publikacji: EN

Abstrakty

EN

In the class Co(p), p ∈ (0,1) of univalent concave functions with a pole at p we find some estimates on the third coefficient as well as the residuum of a function, while its second coefficient is fixed.

Słowa kluczowe

EN

univalent function; concave function; real coefficient

PL

funkcja jednolistna; funkcja wklęsła; współczynnik rzeczywisty

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Journal of Mathematics and Applications
• Rocznik: 2010
• Tom: Vol. 32
• Strony: 109--116
• Opis fizyczny: Bibliogr. 8 poz., wykr.

Twórcy

autor

Zaprawa P.

• Departament of Applied Mathematics, Lublin University of Technology, Nadbystrzycka 38D, 20-618 Lublin, Poland,

Bibliografia

• [1] Avkhadiev F.G., Pommerenke Ch., Wirths K.J., On the coefficients of concave univalent functions. Math. Nachr. 271, 3-9 (2004).
• [2] Avkhadiev F.G., Pommerenke Ch., Wirths K.J., Sharp inegualities for the coefficients of concave schlicht functions. Cumment. Math. Helv. 81, 801-807 (2006).
• [3] Avkhadiev F.G., Wirths K.J., A proof of the Livingstone conjecture. Forum Math. 19, 149-157 (2007).
• [4] Livingstone A.E., Convex meromorphic functions. Ann. Poi. Math. 59, No.3, 275-291 (1994).
• [5] Miller J., Convex and starlike meromorphic functions. Proc. Am. Math. Soc. 80, 607-613 (1980).
• [6] Privalov I.L, Introduction to the Theory of Functions of a Complex Variable, GITTL, Moscow-Leningrad, 1948.
• [7] Wirths K.J., A proof of the Livingston conjecture for the fourth and the fifth coefficient of concave univalent functions Ann. Poi. Math. 83, 87-93 (2004).
• [8] Wirths K.J., On the residuum of concave univalent functions. Serdica Math. J. 32, 209-214 (2006).