On certain applications of differential subordinations for $\Phi$-like functions

Authors

  • V. Ravichandran
  • N. Magesh
  • R. Rajalakshmi

DOI:

https://doi.org/10.5556/j.tkjm.36.2005.126

Abstract

Let $ f(z) $ be a normalized analytic function in $ \Delta=\{z | z\in{\Bbb C} \mbox{ and } |z| <1\} $ satisfying $ f(0)=0 $ and $ f'(0)=1 $. Let $ \Phi $ be an analytic function in a domain containing $ f(\Delta) $, with $ \Phi(0) = 0 $, $ \Phi^{'}(0) = 1 $ and $ \Phi(\omega)\neq 0 $ for $ \omega\in f(\Delta) - \{ 0 \} $. Let $ q(z) $ be a fixed analytic function in $ \Delta$, $q(0)=1 $. The function $ f $ is called $\Phi$-like with respect to $ q $ if

$$ \frac{zf^{'}(z)}{\Phi(f(z))} \prec q(z) \quad (z\in\Delta). $$

In this paper, we obtain some sufficient conditions for functions to be $ \Phi $-like with respect to $ q(z) $.

Author Biographies

V. Ravichandran

Department of Computer Applications, Sri Venkateswara College of Engineerig, Pennalur, Sripermubudur 602 105, India.

N. Magesh

Department of Mathematics, Adhiyamaan College of Engineering, Hosur 635 109, India.

R. Rajalakshmi

Department of Applied Mathematics, Faculty of Natural Sciences, Debub University, Awassa, Ethiopia.

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Published

2005-06-30

How to Cite

Ravichandran, V., Magesh, N., & Rajalakshmi, R. (2005). On certain applications of differential subordinations for $\Phi$-like functions. Tamkang Journal of Mathematics, 36(2), 137-142. https://doi.org/10.5556/j.tkjm.36.2005.126

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