Author

• Bulent Nafi Ornek

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

Abstract

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.

Keywords

• Analytic function
• Schwarz lemma
• Caratheodory's inequality