On complex mappings harmonic in the unit disc with some coefficient conditions

• Autorzy: Łazińska Anna
• Języki publikacji: EN

Abstrakty

EN

Let h = u + w, where u,v are real harmonic functions in the unit disc delta. Such functions are called complex mappings harmonic in delta. The function h may be written in the form h = f + g, where f, g are functions holomorphic in the unit disc, of course. Studies of complex harmonic functions were initiated in 1984 by J. Clunie and T. Sheil-Small ([CS-S]) and were continued by many others mathematicians. We can find some papers on functions harmonic in delta, satisfying certain coefficient conditions, e.g. [AZ], [S], [G]. We investigate some more general problems, which appeared during the seminar conducted by Professor Z. Jakubowski.

Słowa kluczowe

EN

harmonic functions; starlikeness; radius of convexity

PL

funkcje harmoniczne; gwiaździstość

• Wydawca: Oficyna Wydawnicza Politechniki Rzeszowskiej
• Czasopismo: Zeszyty Naukowe Politechniki Rzeszowskiej. Matematyka
• Rocznik: 2002
• Tom: z. 26 [199]
• Strony: 107--116
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Łazińska Anna

• Chair of Special Functions, University of Łódź

Bibliografia

• [AZ] Y. Avci, E. Złotkiewicz, On harmonie univalent mappings, Ann. Univ. Mariae Curie-Skłodowska, Sec. A, XLIV (1) (1990), 1-7.
• [CS-S] J. Clunie, T. Sheil- Small, Harmonie univalent mappings, Ann. Acad. Sci. Fenn., Ser. A. I. Math., 9 (1984), 3-25.
• [D] P. Duren, Univalent funetions, Springer-Verlag, New York- Berlin - Heidelberg - Tokyo, (1983).
• [G] A. Ganczar, On harmonie univalent funetions with small coef¬fieients, Demonstratio Math., XXXIV (3) (2001), 549-558.
• [S] H. Silverman, Harmonie univalent mappings with negative coeffieients, J. Math. Anal. Appl., 220 (1998), 283-289.