Complex Analysis: Theory and Applications · Problem 8.7.10

Conformal Mapping — Howell & Matthews

Mathematics — Complex Analysis · rouche-theorem-univalent-functions

Problem

Suppose that

f(z)

is analytic inside and on the simple closed contour

C

. If

f(z)

is a one-to-one function at points

z

C

, then prove that

f(z)

is one-to-one inside

C

. Hint: Consider the image of

C