D. VAROL, Melike AYDOGAN, S. OWA

SOME RESULTS ON A SUBCLASS OF HARMONIC MAPPINGS OF ORDER ALPHA

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 = b1z + ∑∞ n=2 bnz n , b1 zh′ z − zg′ z h z + g z − 1 − b1 1 + b1 1 − b1 1 + b1 − α, z ∈ U, 0 6 α

Keywords:

Harmonic Mappings, Subordination principle, Distortion theorem,

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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).
R.J. Libera, Some Radius of Convexity Problem, Duke Math. J.31(1964) 143-157.
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.