Article - postprint
We prove an inverse function theorem of the Nash-Moser type. The main difference between our method and that of  is that we use continuous steepest descent while  uses a combination of Newton type iterations and approximate inverses. We bypass the loss of derivatives problem by working on finite dimensional subspaces of infinitely differentiable functions.
© 2001 Elsevier
Castro, Alfonso and J. W. Neuberger. “An inverse function theorem via continuous Newton’s method”, Nonlinear Analysis 47 (2001), pp. 3223-3229.