Even coefficient estimates for bounded univalent functions

• Autorzy: D. V. Prokhorov
• Języki publikacji: EN

Abstrakty

EN

Extremal coefficient properties of Pick functions are proved. Even coefficients of analytic univalent functions f with |f(z)| < M, |z| < 1, are bounded by the corresponding coefficients of the Pick functions for large M. This proves a conjecture of Jakubowski. Moreover, it is shown that the Pick functions are not extremal for a similar problem for odd coefficients.

Słowa kluczowe

EN

coefficient estimates; univalent function; Pick function; Koebe function

Kategorie tematyczne

• 30C50: Coefficient problems for univalent and multivalent functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 3
• Strony: 267-273

Daty

wydano

1993

otrzymano

1992-07-07

Twórcy

autor

D. V. Prokhorov

• Faculty of Mathematics and Mechanics, Saratov State University, Astrakhanskaya, 83 410071 Saratov, Russia

Bibliografia

• [1] L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152.
• [2] D. Bshouty, A coefficient problem of Bombieri concerning univalent functions, Proc. Amer. Math. Soc. 91 (1984), 383-388.
• [3] V. G. Gordenko, Sixth coefficient estimate for bounded univalent functions, in: Theory of Functions and Approximation, Proc. 6th Saratov Winter School, Saratov (in Russian), to appear.
• [4] Z. Jakubowski, On some extremal problems in classes of bounded univalent functions, Zeszyty Nauk. Politechn. Rzeszowskiej Mat. Fiz. 16 (2) (1984), 9-16 (in Polish).
• [5] C. Pommerenke, Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975.
• [6] D. V. Prokhorov, Value sets of systems of functionals in classes of univalent functions, Mat. Sb. 181 (12) (1990), 1659-1677 (in Russian).
• [7] D. V. Prokhorov, Reachable Set Methods in Extremal Problems for Univalent Functions, Izdat. Saratov. Univ., 1992.