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Abstrakty
The functional |c₄ + pc₂c₃ + qc³₂| is considered in the class 𝕊 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.
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Kategorie tematyczne
Czasopismo
Rocznik
Tom
Numer
Strony
7-12
Opis fizyczny
Daty
wydano
1996
otrzymano
1993-10-12
poprawiono
1995-03-15
Twórcy
autor
- Department of Physics&Math., Saratov Pedagogical Institute, 92 Michurin St., Saratov 410071, Russia
autor
- Department of Math.&Mech., Saratov State University, 83 Astrakhanskaya St., Saratov 410071, Russia
Bibliografia
- [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.
Typ dokumentu
Bibliografia
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