Caratheodory's Inequality on the Right half plane

Document Type : Research Paper


Department of Computer Engineering, Amasya University, Merkez-Amasya 05100, Turkey


In this paper, a boundary version of Caratheodory's inequality on the right half plane is investigated. $Z(s)$ is an analytic function defined in the right half of the $s$-plane.We derive inequalities for the modulus of $Z(s)$ function, $|Z′(0)|$, by assuming the $Z(s)$ function is also analytic at the boundary point $s = 0$ on the imaginary axis and finally, the sharpness of these inequalities are proved.


Volume 11, Issue 1
April 2020
Pages 247-258
  • Receive Date: 05 April 2019
  • Revise Date: 02 February 2020
  • Accept Date: 05 February 2020