Classes with negative coefficients and starlike with respect to other points II

Authors

  • Suzeini Abdul Halim
  • Aini Janteng
  • Maslina Darus

DOI:

https://doi.org/10.5556/j.tkjm.37.2006.148

Abstract

A class $ S_{s}^{\star}T(\alpha,\beta,\sigma,k) $ of functions $ f $ which are analytic and univalent in the open unit disk $ {D=\{z:|z|<1\}} $ given by $ f(z)=z-{\sum_{n=2}^{\infty}}{a_n}{z^n} $ and satisfying the condition

$ \abs{\frac{zf'(z)}{f(z)-f(-z)}-k}<\beta \abs{\frac{\alpha zf'(z)}{f(z)-f(-z)}-(2\sigma-k)} $

for $ 0\leq \alpha \leq 1,0< \beta\leq1,0 \leq \sigma \leq \frac{1}{2}$ is introduced and studied. An analogous class $ S_{c}^{\star}T(\alpha,\beta,\sigma,k) $ and $ S_{sc}^{\star}T(\alpha,\beta,\sigma,k) $ are also examined.

Author Biographies

Suzeini Abdul Halim

Institute of Mathematical Sciences , Universiti Malaya, 50603 Kuala Lumpur, Malaysia.

Aini Janteng

Institute of Mathematical Sciences , Universiti Malaya, 50603 Kuala Lumpur, Malaysia.

Maslina Darus

School of Mathematical Sciences, Faculty of Sciences and Technology, Universiti Kebangsaan Malaysia, 43600 Bangi, Selangor, Malaysia.

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Published

2006-12-31

How to Cite

Halim, S. A., Janteng, A., & Darus, M. (2006). Classes with negative coefficients and starlike with respect to other points II. Tamkang Journal of Mathematics, 37(4), 345-354. https://doi.org/10.5556/j.tkjm.37.2006.148

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