# On the estimate of the fourth-order homogeneous coefficient functional for univalent functions

Larisa Gromova; Alexander Vasil'ev

Annales Polonici Mathematici (1996)

- Volume: 63, Issue: 1, page 7-12
- ISSN: 0066-2216

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topLarisa Gromova, and Alexander Vasil'ev. "On the estimate of the fourth-order homogeneous coefficient functional for univalent functions." Annales Polonici Mathematici 63.1 (1996): 7-12. <http://eudml.org/doc/262791>.

@article{LarisaGromova1996,

abstract = {The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class of all univalent holomorphic functions $f(z) = z + ∑^\{∞\}_\{n=2\} c_n z^n$ in the unit disk. For real values p and q in some regions of the (p,q)-plane the estimates of this functional are obtained by the area method for univalent functions. Some new regions are found where the Koebe function is extremal.},

author = {Larisa Gromova, Alexander Vasil'ev},

journal = {Annales Polonici Mathematici},

keywords = {univalent function; area method; univalent functions; estimates of coefficients},

language = {eng},

number = {1},

pages = {7-12},

title = {On the estimate of the fourth-order homogeneous coefficient functional for univalent functions},

url = {http://eudml.org/doc/262791},

volume = {63},

year = {1996},

}

TY - JOUR

AU - Larisa Gromova

AU - Alexander Vasil'ev

TI - On the estimate of the fourth-order homogeneous coefficient functional for univalent functions

JO - Annales Polonici Mathematici

PY - 1996

VL - 63

IS - 1

SP - 7

EP - 12

AB - The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class of all univalent holomorphic functions $f(z) = z + ∑^{∞}_{n=2} c_n z^n$ in the unit disk. For real values p and q in some regions of the (p,q)-plane the estimates of this functional are obtained by the area method for univalent functions. Some new regions are found where the Koebe function is extremal.

LA - eng

KW - univalent function; area method; univalent functions; estimates of coefficients

UR - http://eudml.org/doc/262791

ER -

## References

top- [1] Z. J. Jakubowski, H. Siejka and O. Tammi, On the maximum of a₄ - 3a₂a₃ + μa₂ and some related functionals for bounded real univalent functions, Ann. Polon. Math. 46 (1985), 115-128. Zbl0596.30026
- [2] J. Ławrynowicz and O. Tammi, On estimating of a fourth order functional for bounded univalent functions, Ann. Acad. Sci. Fenn. Ser. AI 490 (1971), 1-18. Zbl0226.30015
- [3] N. A. Lebedev, Area Principle in the Theory of Univalent Functions, Nauka, Moscow, 1975 (in Russian). Zbl0747.30015
- [4] P. Lehto, On fourth-order homogeneous functionals in the class of bounded univalent functions, Ann. Acad. Sci. Fenn. Ser. AI Math. Dissertationes 48 (1984). Zbl0523.30014
- [5] K. Włodarczyk, On certain non-homogeneous combinations of coefficients of bounded univalent functions, Demonstratio Math. 16 (1983), 919-924. Zbl0586.30014

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