Melike AYDOGAN

HARMONIC MAPPINGS RELATED TO STARLIKE FUNCTION OF COMPLEX ORDER α

ISSN: 2146-1147
Başlangıç: 2010
Yayıncı: Turkic World Mathematical Society

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]

Keywords:

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

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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.