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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Fall 2013 • Question 9

Question

Math 6210 • Real Analysis Fall 2013 • Question 9

Let \(D=\{z\in \mathbb C:|z|<1\}\), and let \(f:D\to D\) be an analytic function. Show that \[ |f(z)-f(0)|\le |z(1-\overline {f(0)}f(z))| \] for all \(z\in D\).

Raw LaTeX

Let \(D=\{z\in\mathbb C:|z|<1\}\), and let \(f:D\to D\) be an
analytic function. Show that
\[
|f(z)-f(0)|\le |z(1-\overline{f(0)}f(z))|
\]
for all \(z\in D\).

Topic Tags

Analytic Continuation and Monodromy Holomorphic Functions and Cauchy-Riemann Equations