GENERALIZED CLASS OF UNIVALENT FUNCTIONS WITH TWO FIXED POINTS

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Published: Mar 1, 1993
DOI: https://doi.org/10.5556/j.tkjm.24.1993.4475
Keywords:
Univalent functions starlike, convex extreme points

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B. A. URALEGADDI
Department of Mathematics, Karnatak University, Dharwad-580003, India.
C. SOMANATHA
Department of Mathematics, Karnatak University, Dharwad-580003, India.

Abstract




Univalent functions of the form


\[ f(z)= a_1z-\sum_{n=2}^\infty a_nz^n\]


where $a_n \ge 0$, are dealt with. We examine the subclasses for which $(1 - \lambda)f(z_0)/z_0+\lambda f'(z_0) =1$ ($-1 <z_0 <1$). The coefficient inequali- ties and the extreme points of the classes that are starlike and convex of order o are determined. Many of the results of Silverman are obtained as particular cases.




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How to Cite
URALEGADDI, B. A., & SOMANATHA, C. (1993). GENERALIZED CLASS OF UNIVALENT FUNCTIONS WITH TWO FIXED POINTS. Tamkang Journal of Mathematics, 24(1), 57–66. https://doi.org/10.5556/j.tkjm.24.1993.4475
Issue
Vol. 24 No. 1 (1993)
Section
Papers
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References

H. Silverman, "Univalent functions with negative coefficients", Proc. Amer. Math. Soc. 51 (1975), 109-116.

H. Silverman, "Extreme points of univalent functions with two fixed points", Trans. Amer. Math. Soc. 219 {1976), 387-395.