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Mathematics Qualifying Exam Question Bank

Department of Mathematics

Question

Math 6210 • Real Analysis

Spring 2013 • Question 10

Question

Math 6210 • Real Analysis Spring 2013 • Question 10

Let \(f\) be a holomorphic function in a neighborhood of the closed unit disk centered at \(0\). Assume that \(|f(z)|<1\) for any \(z\) on the unit circle centered at \(0\). How many fixed points does \(f\) have inside this unit circle?

Raw LaTeX

Let \(f\) be a holomorphic function in a neighborhood of the closed
unit disk centered at \(0\). Assume that \(|f(z)|<1\) for any \(z\) on the unit
circle centered at \(0\). How many fixed points does \(f\) have inside this unit
circle?

Topic Tags

Holomorphic Functions and Cauchy-Riemann Equations Holomorphic Roots and Logarithms Zeros of Holomorphic Functions and the Identity Theorem