Sharpened forms of the generalized Schwarz inequality on the boundary

摘要

In this paper, a boundary version of the Schwarz inequality is investigated. We obtain more general results at the boundary. If we know the second coefficient in the expansion of the function $f(z) = 1 + c_{p}z^{p} + c_{p+1}z^{p+1} ldots$, then we obtain new inequalities of the Schwarz inequality at boundary by taking into account $c_{p+1}$ and zeros of the function e?‘“(e?‘§) a?’ 1. The sharpness of these inequalities is also proved.