New properties of some families of holomorphic functions of several complex variables

• Autorzy: Leś-Bomba E. , Liczberski P.
• Języki publikacji: EN

Abstrakty

EN

The paper concerns holomorphic functions in complete bounded n-circular domains of the space Cn and presents some properties of the above mentioned functions belonging to the families described by some geometrical or analytical conditions. This subject has been considered by many mathematicans, for example I.I. Bavrin, K. Dobrowolska, I. Dziubiński, S. Fukui, Z. J. Jakubowski, J. Kamiński, A. Marchlewska, Y. Michiwaki, J. A. Pfaltzgraff, R. Sitarski, T. J. Suffridge, J. Stankiewicz, I. Weinberg, A. Wrzesień, Ł. Żywień and the authors.

Słowa kluczowe

EN

holomorphic functions; Minkowski function; distortion theorem

PL

funkcje holomorficzne; funkcja Minkowskiego; twierdzenie afiniczne przekształceń

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2009
• Tom: Vol. 42, nr 3
• Strony: 491--503
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Leś-Bomba E.

autor

Liczberski P.

• Institute of Mathematics University of Rzeszów Al. Rejtana 16 A2 35-310 Rzeszów, Poland,

Bibliografia

• [1] I. I. Bavrin, A class of regular bounded functions in the case of several complex variables and extremal problems in that class, Moskov Obl. Ped. Inst., Moscov (1976), 1-69, (in Russian).
• [2] I. I. Bavrin, Generalization of functions, regular in the disc and close-to-starlike, to the case of several complex variables, Anal. Math. 5 (1979), 257-267, (in Russian).
• [3] I. I. Bavrin, Sharp estimates in classes of Schur and Caratheodory functions, Dokl. Akad. Nauk 399 (2004), 443-445, (in Russian).
• [4] M. Biernacki, Sur la représenation conforme des domaines linéairement accesibles, Prace Mat-Fiz. 44 (1938), 239-314.
• [5] K. Dobrowolska, I. Dziubiński, On starlike and convex functions of many variables, Demonstratio Math. 11 (1978), 545-555.
• [6] P. L. Duren, Univalent Functions, Springer-Verlag, New York, Heidelberg, Berlin (1983).
• [7] I. Dziubiński, R. Sitarski, On classes of holomorphic functions of many variables starlike and convex on some hypersurfaces, Demonstratio Math. 13 (1980), 619-632.
• [8] S. Fukui, On the estimates of coefficients of analytic functions, Sci. Rep. Tokyo Kyoiku Daigaku, Sect. A 10 (1969), 216-218.
• [9] Z. J. Jakubowski, J. Kamiński, On some classes of Mocanu-Bazilevic functions, Acta Univ. Łodź Folia Math. 5 (1992), 39-62.
• [10] W. Kaplan, Close-to-convex schlicht functions, Michigan Math. J. 1 (1952), 169-185.
• [11] E. Leś-Bomba, P. Liczberski, On some family of holomorphic functions of several complex variables, Sci. Bull. Chełm, Sec. Math. and Comput. Sci. 2 (2007), 7-16.
• [12] Z. Lewandowski, Sur l’identite de certaines classes de functions univalentes, part. I, Ann. Univ. Mariae Curie-Skłodowska Sect. A 12 (1958), 131-146; part. II, 14 (1960), 19-46.
• [13] P. Liczberski, On Bavrin’s families MG,NG of analytic functions of two complex variables, Bull. Techn. Sci. Univ. Łodź 20 (1988), 29-37, [in German].
• [14] P. Liczberski, A. Wrzesień, On some application of a generalized Jack lemma, III Environ. Math. Conf. Jawor 1994, Folia Sci. Univ. Techn. Rzeszow 17 (1995), 25-27.
• [15] A. Marchlewska, On certain subclasses of Bavrin’s families of holomorphic maps of two complex variables, Proc. of the V Environ. Math. Conf. Lesko 1998, Lublin Catholic Univ. Press, Lublin 1999, 99-106.
• [16] Y. Michiwaki, Note on some coefficients in a starlike functions of two complex variables, Res. Rep. Nagaoka Tech. College 1 (1963), 151-153.
• [17] J. A. Pfaltzgraff, T. J. Suffridge, An extension theorem and linear invariant families generated by starlike maps, Ann. Univ. Mariae Curie-Skłodowska Sect. A 53 (1999), 193-207.
• [18] M. O. Reade, On close-to-convex univalent functions, Michigan Math. J. 2 (1955), 59-62.
• [19] W. Rudin, Function Theory in the Unit Ball of Cn, Springer-Verlag, New York, Heidelberg, Berlin (1980).
• [20] J. Stankiewicz, Functions of two complex variables regular in halfspace, Folia Sci. Univ. Techn. Rzeszow 19 (1996), 107-116.
• [21] I. Wainberg, Ł. Żywień, On some two-parameter family of holomorphic functions of two complex variables, Bull. Techn. Sci. Univ. Łodź 15 (1982), 85-104.
• [22] A. A. Temljakov, Integral representation of functions of two complex variables, Izv. Akad. Nauk SSSR. Ser. Mat. 21 (1957), 89-92, (in Russian).