MathDB

9. Let

w=f(x)

be regular in

\left | z \right |\leq 1

. For

0\leq r \leq 1

, denote by c, the image by

f(z)

of the circle

\left | z \right | = r

. Show that if the maximal length of the chords of

c_{1}

1

, then for every

r

such that

0\leq r \leq 1

, the maximal length of the chords of c, is not greater than

r

. (F. 1)

Problem Statement