On functions satisfying more than one equation of Schiffer type

• Autorzy: J. Macura , J. Śladkowska
• Języki publikacji: EN

Abstrakty

EN

The paper concerns properties of holomorphic functions satisfying more than one equation of Schiffer type ($D_n$-equation). Such equations are satisfied, in particular, by functions that are extremal (in various classes of univalent functions) with respect to functionals depending on a finite number of coefficients.

Słowa kluczowe

EN

univalent function; coefficient region; Schiffer type equation

Kategorie tematyczne

• 30C45: Special classes of univalent and multivalent functions (starlike, convex, bounded rotation, etc.)

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1993
• Tom: 58
• Numer: 3
• Strony: 237-252

Daty

wydano

1993

otrzymano

1992-01-02

poprawiono

1992-07-07

poprawiono

1992-12-28

Twórcy

autor

J. Macura

• Institute of Mathematics, Silesian Technical University, Zwycięstwa 42, 44-100 Gliwice, Poland

autor

J. Śladkowska

• Institute of Mathematics, Silesian Technical University, Zwycięstwa 42, 44-100 Gliwice, Poland

Bibliografia

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• [2] Y. Kubota, On extremal problems which correspond to algebraic univalent functions, Kodai Math. Sem. Rep. 25 (1973), 412-428.
• [3] Z. J. Jakubowski and W. Majchrzak, On functions realizing the maximum of two functionals at a time, Serdica 10 (1984), 337-343.
• [4] A. Rost and J. Śladkowska, Sur les fonctions de Bieberbach-Eilenberg satisfaisant à plus qu'une équation de type de Schiffer, Demonstratio Math., to appear.
• [5] H. L. Royden, The coefficient problem for bounded schlicht functions, Proc. Nat. Acad. Sci. U.S.A. 35 (1949), 637-662.
• [6] A. C. Schaeffer and D. C. Spencer, Coefficient Regions for Schlicht Functions, Amer. Math. Soc., 1950.
• [7] J. Śladkowska, Sur les fonctions univalentes, bornées, satisfaisant deux au moins $D_n$-équations, Demonstratio Math. 11 (1978), 1-28.
• [8] V. V. Starkov, Bounded univalent functions realizing the extrema of two coefficients functionals at a time, in: Proc. XIth Instructional Conf. on the Theory of Extremal Problems, Łódź 1990, 31-33.
• [9] K. Tochowicz, Functions which satisfy the differential equation of Schiffer type, Zeszyty Nauk. Politechn. Rzeszowskiej Mat. Fiz. 38 (6) (1987), 103-113.