On norm estimation for certain subclasses of analytic functions in geometric functions theory

Document Type : Research Paper

Author

Department of Mathematics, Payame Noor University, P.O.Box 19395-3697, Tehran, Iran

Abstract

We investigate on some subclasses of analytic fuctions defined by subordination. Also, we give estimates of $\sup_{|z|<1}\big(1-|z|^{2}\big)\big|\dfrac{f^{''}(z)}{f^{'}(z)}\big|$, for functions belonging to extended class of starlike functions. For a locally univalent analytic function $f$ defined on $\Delta =\{z\in \mathbb{C}: |Z|<1\}$, we consider the pre-Schwarzian norm by $\Vert T\Vert=\sup _{|z|<1}\big(1-|z|^{2}\big)\big|\dfrac{f^{''}(z)}{f^{'}(z)}\big|$. In this work, we find the sharp norm estimate for the functions $f$ in the extended classes of starlike functions.

Keywords

References

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History

  • Receive Date: 05 May 2022
  • Revise Date: 25 September 2022
  • Accept Date: 10 October 2022

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