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Liczberski–Starkov gave a sharp lower bound for ‖DΦn(f)(z)‖ near the origin, where Φn is the Roper–Suffridge extension operator and f is a normalized convex mapping on the unit disk in C. They gave a conjecture that the sharp lower bound holds on the Euclidean unit ball Bn in Cn. In this paper, we will give a sharp lower bound on Bn for a more general extension operator and for normalized univalent...
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