Even coefficient estimates for bounded univalent functions

D. V. Prokhorov

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 3, page 267-273
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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D. V. Prokhorov. "Even coefficient estimates for bounded univalent functions." Annales Polonici Mathematici 58.3 (1993): 267-273. <http://eudml.org/doc/262483>.

@article{D1993,
abstract = {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.},
author = {D. V. Prokhorov},
journal = {Annales Polonici Mathematici},
keywords = {coefficient estimates; univalent function; Pick function; Koebe function; bounded univalent functions; conjecture of Jakubowski},
language = {eng},
number = {3},
pages = {267-273},
title = {Even coefficient estimates for bounded univalent functions},
url = {http://eudml.org/doc/262483},
volume = {58},
year = {1993},
}

TY - JOUR
AU - D. V. Prokhorov
TI - Even coefficient estimates for bounded univalent functions
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 3
SP - 267
EP - 273
AB - 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.
LA - eng
KW - coefficient estimates; univalent function; Pick function; Koebe function; bounded univalent functions; conjecture of Jakubowski
UR - http://eudml.org/doc/262483
ER -

References

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  1. [1] L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152. Zbl0573.30014
  2. [2] D. Bshouty, A coefficient problem of Bombieri concerning univalent functions, Proc. Amer. Math. Soc. 91 (1984), 383-388. Zbl0571.30019
  3. [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. [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). Zbl0579.30022
  5. [5] C. Pommerenke, Univalent Functions, Vandenhoeck and Ruprecht, Göttingen, 1975. 
  6. [6] D. V. Prokhorov, Value sets of systems of functionals in classes of univalent functions, Mat. Sb. 181 (12) (1990), 1659-1677 (in Russian). Zbl0717.30013
  7. [7] D. V. Prokhorov, Reachable Set Methods in Extremal Problems for Univalent Functions, Izdat. Saratov. Univ., 1992. Zbl0814.30016

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