# Even coefficient estimates for bounded univalent functions

Annales Polonici Mathematici (1993)

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

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topD. 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

top- [1] L. de Branges, A proof of the Bieberbach conjecture, Acta Math. 154 (1985), 137-152. Zbl0573.30014
- [2] D. Bshouty, A coefficient problem of Bombieri concerning univalent functions, Proc. Amer. Math. Soc. 91 (1984), 383-388. Zbl0571.30019
- [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). Zbl0579.30022
- [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). Zbl0717.30013
- [7] D. V. Prokhorov, Reachable Set Methods in Extremal Problems for Univalent Functions, Izdat. Saratov. Univ., 1992. Zbl0814.30016

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