The originator of the fixed point theorem for DCPOs
The non-constructive version of Pataraia's theorem is called the Bourbaki-Witt fixed point theorem. I learned it from Davey and Priestley's Introduction to Lattices and Order, and Wikipedia gives the following references:


Nicolas Bourbaki (1949). "Sur le théorème de Zorn". Archiv der Mathematik. 2: 434–437. doi:10.1007/bf02036949. 
Ernst Witt (1951). "Beweisstudien zum Satz von M. Zorn". Mathematische Nachrichten. 4: 434–438. doi:10.1002/mana.3210040138. 


However, as usual, some classically equivalent formulations of this theorem become distinguishable constructively. Andrej Bauer and Peter Lumsdaine have a very nice paper about this, On the Bourbaki-Witt Principle in Toposes, where they examine these issues in detail.