The most common proof of the Inverse Function Theorem in textbooks relies on the Banach fixed-point theorem.

QUESTION. It is possible to say, using historical references, which mathematician came up with the idea of using Banach's Contraction Principle to prove the inverse function theorem? If not, what is the earliest known source where such proof appeared?

I did a search on the Mathematics history books specialized in the subject, but I did not find any clues. For example:

  • $\begingroup$ Hi MathOverview, and welcome to HSM. Please note that crossposting on different SE sites is not encouraged. Instead, one should flag the original post and ask the moderators for a migration. $\endgroup$ – Danu Jun 26 '15 at 7:15
  • $\begingroup$ @Danu So I must ask the MSE moderators to migrate my original question in MSE for HSM? $\endgroup$ – MathOverview Jun 27 '15 at 13:51
  • $\begingroup$ Yes, that would be the correct way to proceed. $\endgroup$ – Danu Jun 27 '15 at 15:20

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