CERTAIN CLASSES OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS

Authors

  • NAK EUN CHO Department of Applied Mathematics, National Fisheries University of Pusan, Pusan 608-737, Korea.
  • JI A KIM Department of Applied Mathematics, National Fisheries University of Pusan, Pusan 608-737, Korea.

DOI:

https://doi.org/10.5556/j.tkjm.25.1994.4452

Keywords:

Hadamard product, extreme points, radius of convexity, closure theorems

Abstract

Let $\Sigma_p$ denote the class of functions of the form

\[f(z)=\frac{a_{-1}}{z}+\sum_{k=1}^\infty a_kz^k \quad (a_k\ge 0, a_{-1}>0)\]

which are analytic in the annulus $D =\{z |0< |z|<1\}$. Let $\Sigma_{p,1}$ and $\Sigma_{p,2}$ denote subclasses of $\Sigma_p$ satisfying $f(z_0)=1/z_0$ and $f'(z_0)=-1/z^2_0$ ($-1<z_0<1$, $z_0\neq 0$), respectively. Properties of certain subclasses of $\Sigma_{p,1}$ and $\Sigma_{p,2}$ are investigated and sharp results are obtained. Also a new characterization for certain subclass of $\Sigma_p$ is proved.

References

M. L. Mogra, T.R. Reddy and O.P. Juneja, "Meromorphic univalent functions with positive coefficients, "Bull. Austral. Math. Soc., 32(1985), 161-176. ,

N. E. Cho, "On certain class of meromorphic functions with positive coefficients," Math. Japonica, 34(1989), 901-907.

B. A. Uralegaddi and M.D. Ganigi, "A new criterion for meromorphic convex functions," Tamkang J. Math., 19(1988), 43-48.

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

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Published

1994-09-01

How to Cite

CHO, N. E., & KIM, J. A. (1994). CERTAIN CLASSES OF MEROMORPHIC FUNCTIONS WITH POSITIVE COEFFICIENTS. Tamkang Journal of Mathematics, 25(3), 247–256. https://doi.org/10.5556/j.tkjm.25.1994.4452

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Papers