Page "Stefan Banach" Paragraph 18

Likewise, Banach's fixed point theorem, based on earlier methods developed by Charles Émile Picard, was included in his dissertation, and was later extended by his students ( for example in the Banach – Schauder theorem ) and other mathematicians ( in particular Bouwer and Poincaré and Birkhoff ).

The theorem did not require linearity of the space, and applied to any Cauchy space ( complete metric space ).