HARMONIC MAPPINGS RELATED TO STARLIKE FUNCTION OF COMPLEX ORDER α

Yıl 2014, Cilt: 4 Sayı: 1, 7 - 15, 01.06.2014

Melike Aydogan

Öz

Let SH be the class of harmonic mappings defined by SH = { f = h z + g z | h z = z + ∑∞ n=2 anz n , g z = ∑∞ n=1 bnz n } The purpose of this talk is to present some results about harmonic mappings which was introduced by R. M. Robinson [8]

Anahtar Kelimeler

Harmonic Mappings, Subordination principle, Distortion theorem, Growththeorem, Coefficient inequality

Kaynakça

• C. Caratheodory, Uber den Variabilitatsatsbereich der Koezienten von Potenzrei-hen, die gegebene Werte nicht annehmen, Math. Ann. 64 (1907), 95-115.
• Clunie and T. Sheil-Small, Harmonic Univalent functions, Annales Academiae Scientiarum Fennicae, Series A, Vol. 9, pp. 3-35, (1984).
• Duren, P. , Harmonic Mappings in the Plane, Vol. 156 of Cambridge Tracts in Mathematics, Cam- bridge University Press, Cambridge UK, (2004).
• Goodman A. W. , Univalent Functions, Volume I and Volume II, Mariner publishing Company INC, Tampa Florida, (1983).
• Jack, I. S. , Functions starlike and convex of order α, J. London Math. Soc. 3(197), no 2.
• W. Janowski, Some extremal problems for certain families of analytic functions I, Annales Polinici Mathematici 27, (1973), 298-326.
• M. A. Nasr and M. K. Aouf, Starlike functions of complex order, Jour. of Natural science and Math- ematics vol. 25, No.1, (1985), 1-12.
• Robinson, R. M . , Univalent majorants, Trans. Amer. Math. Soc. 61 (1947), 1-35.