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ArticleOriginal scientific text

Title

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

Authors 1, 2

Affiliations

  1. Department of Physics&Math., Saratov Pedagogical Institute, 92 Michurin St., Saratov 410071, Russia
  2. Department of Math.&Mech., Saratov State University, 83 Astrakhanskaya St., Saratov 410071, Russia

Abstract

The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class of all univalent holomorphic functions f(z)=z+∑∞_{n=2}cnzn 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.

Keywords

ENG
univalent function, area method

Bibliography

  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.
  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.
  3. N. A. Lebedev, Area Principle in the Theory of Univalent Functions, Nauka, Moscow, 1975 (in Russian).
  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).
  5. K. Włodarczyk, On certain non-homogeneous combinations of coefficients of bounded univalent functions, Demonstratio Math. 16 (1983), 919-924.
Annales Polonici Mathematici
1996/63/1
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Pages:
7-12
Main language of publication
English
Received
1993-10-12
Accepted
1995-03-15
Published
1996
Exact and natural sciences