Banach Fixed Point Theorem

In this video, I prove the celebrated Banach fixed point theorem, which says that in a complete metric space, a contraction must have a fixed point. The proof is quite elegant and illustrates the beauty of analysis. This theorem is used for example to show that ODE have unique solutions under certain conditions. Enjoy!

Note: The thumbnail was taken from https://en.wikipedia.org/w/index.php?title=File:Cosine_fixed_point.svg

Видео Banach Fixed Point Theorem канала Dr Peyam