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

Abstract

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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.

How to cite

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Larisa 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

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  1. [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. [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. [3] N. A. Lebedev, Area Principle in the Theory of Univalent Functions, Nauka, Moscow, 1975 (in Russian). Zbl0747.30015
  4. [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. [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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