On a new subclass of p-valent functions with negative coefficients
Bu makalede negative katsayılı p − valent analitik fonksiyonların *( , , , , ) pP α β ξ Ω m ile gösterilen yeni bir sınıfı tanıtıldı. *( , , , , ) pP α β ξ Ω m sınıfına ait fonksiyonlar için katsayı teoremi, distorsiyon teoremi ve kapanış teoremi belirlendi. Ayrıca *( , , , , ) pP α β ξ Ω m sınıfı için konvekslik yarıçapı elde edildi. Bundan başka *( , , , , ) pP α β ξ Ω m sınıfına ait
Negatif katsayılı p-valent fonksiyonların bir yeni altsınıfı hakkında
We introduce a new subclass *( , , , , ) pP α β ξ Ω m of analytic and p − valent functions with negative coefficients. Coefficient theorem, distortion theorem and closure theorem of functions belonging to the class *( , , , , ) pP α β ξ Ω m are determined. Also we obtain radius of convexity for * ( , , , , ). pP α β ξ Ω m Integral operators of functions belonging to the class *( , , , , ) pP α β ξ Ω m are studied here. Furthermore the extreme points of *( , , , , ) pP α β ξ Ω m are also determined.
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- [1]. M. K. Aouf, Certain classes of p − valent functions with negative coefficients II, Indian J. Pure Appl. Math. 19 (8), (1988), 761-767.
- [2]. T. R. Caplinger, On certain classes of analytic functions, Ph. D. Thesis University of Mississipi, (1972).
- [3]. V. P. Gupta, P. K. Jain, On certain classes of univalent functions with negative coefficients, Bull. Aust. Math. Soc. 15, (1976), 467-473.
- [4]. O. P. Juneja, M. L. Mogra, radius of convexity for certain classes of univalent analytic functions, Pasific Journal Math. 78, (1978), 359-368.
- [5]. S. R. Kulkarni, Some problems connected with univalent functions, Ph. D. Dissertation Shivaji University Kolhapur (1981).
- [6]. S. R. Kulkarni, M. K. Aouf, S. B. Joshi, On a subfamily of p − valent functions with negative coefficients, Math. Bech. 46 (1994), 71-75.
- [7]. G. S. Salagean, Subclass of univalent functions, Lecture Notes in Math. (springer-Verlag) 1013, (1983), 362-372.
- [8]. H. Orhan and H. Kiziltunç, A generalization on subfamily of p − valent functions with negative coefficients, Appl. Math. Comp. 155 (2004) 521-530.