On some generalization of coefficient conditions for complex harmonic mappings

• Autorzy: Adamczyk G. , Łazińska A.
• Języki publikacji: EN

Abstrakty

EN

Let h = u + iv, where u, v are real harmonic functions in the unit disc A. Such functions are called complex mappings harmonic in A. 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 ([2]) and were continued by many others mathematicians. We can find some papers on functions harmonic in A, satisfying certain coefficient conditions, e.g. [1], [4], [6], [7], [8]. We investigate some more general problem, i. e. a coefficient inequality with any fixed sequence of real positive numbers.

Słowa kluczowe

EN

convexity; harmonic functions; starlikness

PL

funkcje harmoniczne

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2004
• Tom: Vol. 37, nr 2
• Strony: 317--326
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Adamczyk G.

• Chair of Special Functions, Faculty of Mathematics, University of Łódź, ul. S. Banacha 22, 90-238 Łódź

autor

Łazińska A.

• Chair of Special Functions, Faculty of Mathematics, University of Łódź, ul. S. Banacha 22, 90-238 Łódź

Bibliografia

• [1] Y. Avci, E. Złotkiewicz, On harmonic univalent mappings, Ann. Univ. Mariae Curie-Skłodowska, Sec. A , XLIV (1) (1990), 1-7.
• [2] J. Clunie, T. Sheil-Small, Harmonic univalent mappings, Ann. Acad. Sci. Fenn., Ser. A. I. Math., 9 (1984), 3-25.
• [3] P. Duren, Univalent Functions, Springer-Verlag, New York-Berlin-Heidelberg-Tokyo, (1983).
• [4] A. Ganczar, On harmonic univalent functions with small coefficients, Demonstratio Math. 34 (3) (2001), 549-558.
• [5] A. Łazińska, On complex mappings harmonic in the unit disc with some coefficient conditions, Folia Sci. Univ. Technicae Resoviensist Mat. z. 26, 199 (2002), 107-116.
• [6] T. Rosy, H. Silverman, B. A. Stephen, K. G. Subramanian, Subclasses of harmonic starlike functions, J. Analysis 9 (2001), 99-108.
• [7] H. Silverman, Harmonic univalent mappings with negative coefficients, J. Math. Anal. Appl. 220 (1998), 283-289.
• [8] J. M. Yahangiri, Coefficient bounds and univalence criteria for harmonic functions with negative coefficients, Ann. Univ. Mariae Curie-Skłodowska, Sec. A, LII (2) (1998), 57-66.