Caratheodory's Inequality on the Right half plane

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′(۰)|, by assuming the Z(s) function is also analytic at the boundary point s = ۰ on the imaginary axis and finally, the sharpness of these inequalities are proved.

Keywords:

Analytic function , Schwarz lemma , Caratheodory's inequality