For each n≥2, let C(n) be the smallest constant such that for any complex polynomial f of degree n≥2 with zeros z1,…,zn in the unit disk and critical points w1,…,wn−1, and for any nonnegative weights l1,…,ln≥0 satisfying ∑k=1nlk=1, we have
1≤j≤n−1mink=1∑nlkzk−wj≤C(n).
It was conjectured by Schmeisser that C(n)=1.