I want to show that the modulus of the automorphism(adsbygoogle = window.adsbygoogle || []).push({});

[tex]\frac{a-z}{1-\overline{a}z}[/tex]

is strictly bounded by 1 in the unit disc. Applying Schwarz lemma gives the result immediately. But I am looking for a straight forward proof for that.

Thanks in advance

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# Automorphisms of the unit disc is less than 1

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