ON A NEW SUBCLASS OF P-VALENT FUNCTIONS WITH NEGATIVE COEFFICIENTS
Abstract
We introduce a new subclass of analytic and valent functions with negative coefficients. Coefficient theorem, distortion theorem and closure theorem of functions belonging to the class are determined. Also we obtain radius of convexity for Integral operators of functions belonging to the class are studied here. Furthermore the extreme points of are also determined.
Keywords
Distortion theorem, exreme points, analytic function, radius of convexity, Salagean operator
References
- M. K. Aouf, Certain classes of p −valent functions with negative coefficients II, Indian J. Pure Appl. Math. 19 (8), (1988), 761-767.
- T. R. Caplinger, On certain classes of analytic functions, Ph. D. Thesis University of Mississipi, (1972).
- V. P. Gupta, P. K. Jain, On certain classes of univalent functions with negative coeffici- ents, Bull. Aust. Math. Soc. 15, (1976), 467-473.
- O. P. Juneja, M. L. Mogra, radius of convexity for certain classes of univalent analytic functions, Pasific Journal Math. 78, (1978), 359-368.
- S. R. Kulkarni, Some problems connected with univalent functions, Ph. D. Dissertation Shivaji University Kolhapur (1981).
- 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.
- G. S. Salagean, Subclass of univalent functions, Lecture Notes in Math. (springer- Verlag) 1013, (1983), 362-372.
- H. Orhan and H. Kiziltunç, A generalization on subfamily of p −valent functions with negative coefficients, Appl. Math. Comp. 155 (2004) 521-530.