Abstract
We study problems similar to the Koebe Quarter Theorem for close-to-convex polynomials with all zeros of derivative in {mathbb {T}}:={zin {mathbb {C}}:|z|=1}. We found minimal disc containing all images of {mathbb {D}}:={zin {mathbb {C}}: |z|<1} and maximal disc contained in all images of {mathbb {D}} through polynomials of degree 3 and 4. Moreover we determine the extremal functions for both problems.
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