Angular Derivatives for Holomorphic Self-Maps of the Disk

Let the function phi be holomorphic in the unit disk D and let phi(D) subset of D. We consider points zeta is an element of partial derivative D where phi has an angular limit phi(zeta) is an element of partial derivative D and study the behaviour of (phi(z)) - phi(zeta))/(z-zeta) as z tends to zeta in various ways. In particular, there is a result connecting vertical bar psi'(zeta(upsilon))vertical bar and vertical bar psi(zeta(mu)) - psi(zeta(upsilon))vertical bar for three points zeta(upsilon) . Expressed as a positive semidefinite quadratic form, this result could, perhaps, be generalized to n points zeta(upsilon) .