Sharp Bounds for Schippers–Schwarzian Derivatives via the Schur-Parameter Method

In the present paper, we derive sharp bounds for Schippers–Schwarzian derivatives of functions belonging to the two core Ma–Minda subclasses associated with the canonical half-plane majorant ψ(z)=1+z1−z: the convex class C(ψ) and starlike class S*(ψ), and the generalized Robertson class SPα(β). All derivations avoid Carathéodory coefficients cn; we only express the Taylor coefficients of Schwarz functions via Schur polynomials Fk(γ1,…,γk), then reduce each functional to a single-variable optimization, and construct explicit extremal Schwarz kernels as well as integral-form extremal univalent mappings.