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

• Autorzy: Larisa Gromova , Alexander Vasil'ev
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

univalent function; area method

Kategorie tematyczne

• 30C55: General theory of univalent and multivalent functions

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1996
• Tom: 63
• Numer: 1
• Strony: 7-12

Daty

wydano

1996

otrzymano

1993-10-12

poprawiono

1995-03-15

Twórcy

autor

Larisa Gromova

• Department of Physics&Math., Saratov Pedagogical Institute, 92 Michurin St., Saratov 410071, Russia

autor

Alexander Vasil'ev

• 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.