ON CERTAIN SUBCLASS OF UNIVALENT FUNCTIONS IN THE UNIT DISC I

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Published: Dec 1, 1995
DOI: https://doi.org/10.5556/j.tkjm.26.1995.4409
Keywords:
Analytic univalent functions close-to-convexity starlikeness

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M. K. AOUF
Department of Mathematics, Facllaty of Science, University of Mansoura, Mansoura, Egypt.
A. SHAMANDY
Department of Mathematics, Facllaty of Science, University of Mansoura, Mansoura, Egypt.
M. F. YASSEN
Department of Mathematics, Facllaty of Science, University of Mansoura, Mansoura, Egypt.

Abstract




The object of the present paper is to derive several interesting proper- ties of the class $P_n(\alpha, \beta, \gamma)$ consisting of analytic and univalent functions with neg- ative coefficients. Coefficient estimates, distortion theorems and closure theorems of functions in the class $P_n(\alpha, \beta, \gamma)$ are determined. Also radii of close-to-convexity, starlikeness and convexity and integral operators are determined.




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How to Cite
AOUF, M. K., SHAMANDY, A., & YASSEN, M. F. (1995). ON CERTAIN SUBCLASS OF UNIVALENT FUNCTIONS IN THE UNIT DISC I. Tamkang Journal of Mathematics, 26(4), 299–312. https://doi.org/10.5556/j.tkjm.26.1995.4409
Issue
Vol. 26 No. 4 (1995)
Section
Papers
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References

H. S. Al-Amiri, "On a subclass of close-to-convex functions with negative coefficients," Mathematica, 31 (54), no.I , 1-7, 1989.

V. P. Gupta and P. K. Jain, "Certain classes of univalent functions with negative coefficients. 11," Bull. Austral. Math. Soc., 15, 467-473, 1976.

S. Owa, "Certain subclasses of univalent functions in the unit disc," Pure Appl. Math. Sci., 22, no.1-2, 1-15, 1985.

G. Salagean, "Subclasses of univalent functions," Lecture notes in Math., (Springer-Verlag) 1013, 362-372, 1983.

S. M. Sarangi and B. A. Uralegaddi, "The radius of convexity and starlikeness for certain classes of analytic functions with negative coefficients. I," Rend. Acad. No,z. Lincei, 65, 38-42, 1978.