On some coefficient conditions for complex harmonic mappings with a pole at the infinity

• Autorzy: Sibelska A.
• Języki publikacji: EN

Abstrakty

EN

In 1984 J. Clunie and T. Sheil-Small initiated studies of complex functions harmonic in the unit disc. In 1987 W. Hergartner and G. Schober considered mappings of this type, defined in the domain U = {z is an element of C : \z\ > 1}. Several mathematicians examine classes of complex harmonic functions with some coefficient conditions, defined in the unit disc (e.g. [2], [5], [10], [1] [9]) or in U (e.g. [8], [7]). We investigate the classes of mappings harmonic in U with coefficient conditions more general than the considered in paper [8].

Słowa kluczowe

EN

harmonic functions; convex functions; starlike functions; extreme points

PL

funkcje harmoniczne; funkcje wypukłe; funkcje gwiaździste; punkty ekstremalne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2006
• Tom: Vol. 39, nr 2
• Strony: 335--346
• Opis fizyczny: Bibliogr. 11 poz.

Twórcy

autor

Sibelska A.

• Faculty of Mathematics University of Łódź, ul. S. Banacha 22, 90-238 Łódź, Poland,

Bibliografia

• [1] G. Adamczyk, A. Łazińska, On some generalization of coefficient coditions for complex harmonic mappings, Demonstratio Math. XXXVII (2) (2004), 317–326.
• [2] Y. Avci, E. Złotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Skłodowska, Sec. A, XLIV (1) (1990), 1–7.
• [3] J. Clunie, T. Sheil-Small, Harmonic univalent mappings, Ann. Acad. Sci. Fenn., Ser. A. I. Math. 9 (1984), 3–25.
• [4] P. Duren, Univalent functions, Springer-Verlag, New York-Berlin-Hiedelberg-Tokyo, (1983).
• [5] A. Ganczar, On harmonic univalent functions with small coefficient , Demonstratio Math. XXXIV (3) (2001), 549–558.
• [6] W. Hengartner, G. Schober, Univalent harmonic functions, Trans. Amer. Math. Soc. 299 (1987), 1–31.
• [7] J.M. Jahangiri, Harmonic meromorphic starlike functions, Bull. Korean. Math. Soc. 37 (2000), no.2, 291–301.
• [8] J.M. Jahangiri, H. Silverman, Meromorphic univalent harmonic functions with negative coefficients, Bull. Korean. Math. Soc. 36 (1999), no. 4, 763–770.
• [9] Z.J. Jakubowski, A. Łazińska, A. Sibelska, On some properties of complex harmonic mappings with a two-parameter coefficient condition, Math. Balkanica, New Series Vol. 18, (2004), Fasc. 3-4, 313–319.
• [10] A. Łazińska, On complex mappings harmonic in the unit disc with some coefficient conditions, Folia Sci. Univ. Technicae Resoviensis, Mat. z. 26, 199 (2002), 107–116.
• [11] A. Sibelska, On some coefficient conditions for harmonic mappings, Materialy Konferencyjne X Środowiskowej Konferencji Matematyczno-Informatycznej, Rzeszow- Lublin-Korytnica, 30.IV- 3.V.2004, p. 53 (in Polish).