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 dened in the right half of the s-plane.We derive inequalities for the modulus of Z(s) function, jZ′(0)j, by assuming the Z(s) function is also analytic at the boundary point s = 0 on the imaginary axis and nally, the sharpness of these inequalities is proved.