On generalization of close-to-convexity for complex holomorphic functions in Cn

• Autorzy: Marchlewska A.
• Języki publikacji: EN

Abstrakty

EN

Sveral authors (I. I. Bawrin [1], K. Dobrowolska, I. Dziubinski, P. Liczberski, R. Sitarski [3], [4], [5], [13], S. Gong, S. S. Miller [6], Z. J. Jakubowski and J. Kaminski [8], J. Janiec [10] and others) studied various families of complex holomorphic functions in Cn and in Banach space, corresponding with famous subclasses of univalent functions. In this paper we study a class of holomorphic functions of n complex variables analogous to the class of close-to-convex functions of one variable considered by M. Biernacki, W. Kaplan and Z. Lewandowski (see [2], [11], [12]).

Słowa kluczowe

EN

holomorphic functions; convex functions; circular domains; close-to-convexity

PL

funkcje holomorficzne; funkcje wypukłe; przestrzeń Banacha

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 4
• Strony: 847--856
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Marchlewska A.

• Faculty of Computer Science, Academy of Humanities and Economocs in Łódź, ul. Rewolucji 1905 r. 64, 90-222 Łódź, Poland

Bibliografia

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• [2] M. Biernacki, Sur la representation conforme des domaines lineairement accessibles, Prace Mat.-Fiz., 44 (1936), 293-314.
• [3] K. Dobrowolska, I. Dziubiński, Of starlike and convex functions of many variables, Demonstratio Math. 11(2), (1978), 545-555.
• [4] K. Dobrowolska, P. Liczberski, On some differential inequalities for holomorphic functions of many variables, Demonstratio Math. 14(2), (1981), 383-398.
• [5] I. Dziubiński, R. Sitarski, On classes of holomorphic functions of many variables starlike and convex on some hipersurfaces, Demonstratio Math. 13(3), (1980), 619-632.
• [6] A. W. Goodman, Univalent functions, Mariner Publishing Company 1983.
• [7] S. Gong, S. S. Miller, Partial differential subordinations and inequalities defined on complete circular domains, Comm. Partial Differential Equations, 11 (1986), No. 11, 1243-1255.
• [8] I. S. Jack, Function starlike and convex of order alpha, J. London Math. Soc. 3 (1971), 469-474.
• [9] Z. J. Jakubowski, J. Kamiński, On some classes of Mocanu-Bazilevic functions, Acta Univ. Lodz., Folia Math., 5 (1992), 39-61.
• [10] E. Janiec, On starlike and convex maps of a Banach space into the complex plane, Demonstratio Math. 27 (1994), 511-516.
• [11] W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1 (1952) 169-185.
• [12] Z. Lewandowski, Sur l 'identite de certaines classes de fonctions univalentes, part I, Ann. Univ. M. Curie-Skłodowska, 12, (1958), 131-146; part II, ibid. 14 (1960), 19-46.
• [13] P. Liczberski, On Bavrin families of holomorphic maps of Banach spaces into the complex plane, Zesz. Nauk. Polit. Rzesz, 48 (1988), 77-85.
• [14] W. Rudin, Function Theory in the Unit Ball, Springer-Verlag, New York Inc., 1980.
• [15] K. Sakaguchi, On certain univalent mapping, J. Math. Soc. Japan 11 (1959), 72-75.
• [16] G. Schober, Univalent Functions - Selected Topics, Springer-Verlag, New York Inc., 1975.