On the Koebe Quarter Theorem for Certain Polynomials of Even Degree

We continue research on problems similar to the Koebe Quarter Theorem for close-to-convex polynomials with all zeros of derivative in \(\mathbb T:=\{z\in \mathbb C:|z|=1\}\) $\mathbb{T}:=\{z\in \mathbb{C}:|z|=1\}$ . We found the minimal disc containing all images of \(\mathbb D:=\{z\in \mathbb C: |z|<1\}\) $\mathbb{D}:=\{z\in \mathbb{C}:|z|<1\}$ and the maximal disc contained in all images of \(\mathbb D\) $\mathbb{D}$ through polynomials of degree 6. Moreover, we determine the extremal functions for both problems. Furthermore, we state the conjecture concerning polynomials of higher even degrees.