Caratheodory's Inequality on the Right half plane

Ornek, Bulent Nafi

doi:10.22075/ijnaa.2020.4274

Caratheodory's Inequality on the Right half plane

Document Type : Research Paper

Author

Bulent Nafi Ornek

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

10.22075/ijnaa.2020.4274

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