On the univalent, bounded, non-vanishing and symmetric functions in the unit disk

• Autorzy: J. Śladkowska
• Języki publikacji: EN

Abstrakty

EN

The paper is devoted to a class of functions analytic, univalent, bounded and non-vanishing in the unit disk and in addition, symmetric with respect to the real axis. Variational formulas are derived and, as applications, estimates are given of the first and second coefficients in the considered class of functions.

Słowa kluczowe

EN

univalent function; variational method; 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: 1996
• Tom: 64
• Numer: 3
• Strony: 291-299

Daty

wydano

1996

otrzymano

1995-12-18

Twórcy

autor

J. Śladkowska

• Institute of Mathematics, Silesian Technical University, Kaszubska 23, 44-100 Gliwice, Poland

Bibliografia

• [1] G. M. Goluzin, Geometric Theory of a Complex Variable, Transl. Math. Monographs 26, Amer. Math. Soc., Providence, R.I., 1969.
• [2] J. A. Hummel and B. Pinchuk, Variations for bounded nonvanishing univalent functions, J. Anal. Math. 44 (1984-85), 183-199.
• [3] J. A. Hummel and M. M. Schiffer, Variational methods for Bieberbach-Eilenberg functions and for pairs, Ann. Acad. Sci. Fenn. Ser. AI Math. 3 (1977), 3-42.
• [4] C. Pommerenke, Univalent Functions, Göttingen, 1975.
• [5] D. V. Prokhorov and J. Szynal, Coefficient estimates for bounded nonvanishing functions, Bull. Acad. Polon. Sci. Sér. Sci. Math. 29 (1981), 223-230.
• [6] J. Śladkowska, Sur une famille des fonctions univalentes et bornées, Demonstratio Math. 22 (1989), 973-982.
• [7] J. Śladkowska, Sur la famille des fonctions univalentes, bornées et symétriques qui n'atteignent pas une valeur fixée, Ann. Polon. Math. 52 (1990), 147-160.
• [8] J. Śladkowska, A variational method for univalent nonvanishing functions in the unit disk, Folia Sci. Univ. Tech. Resov. 129, Math. 16 (1994), 63-77.