Geometric function theory: Difference between revisions

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Then, |''f''(''z'')| ≤ |''z''| for all ''z'' in '''D''' and |''f′''(0)| ≤ 1.
 
Moreover, if |''f''(''z'')| = |''z''| for some non-zero ''z'' or if |''f′''(0)| = 1, then ''f''(''z'') = ''az'' for some ''a'' in '''C''' with |''a''| =(necessarily) equal to 1.</blockquote>
 
===Maximum principle===