Hey guys,

I tried to write a proof for Banach's Contraction Mapping theorem, which is extremely important for fixed-point iteration to numerically solve for the zeroes of an equation, but I think it even extends to PDEs, where a function that solves the PDE is a fixed point in infinite dimensional function spaces. Do you guys think, my proof is rigorous and technically correct?

Cheers,

Quasar.

I tried to write a proof for Banach's Contraction Mapping theorem, which is extremely important for fixed-point iteration to numerically solve for the zeroes of an equation, but I think it even extends to PDEs, where a function that solves the PDE is a fixed point in infinite dimensional function spaces. Do you guys think, my proof is rigorous and technically correct?

Cheers,

Quasar.