Abstract :
We extend the classical inverse and implicit function theorems, the implicit
function theorems of Lyusternik and Graves, and the results of Clarke and
Pourciau to the situation when the given function is not smooth, but it has a convex
strict prederivative whose measure of noncompactness is smaller than its measure
of surjectivity. The proof of the main results requires Banach’s open mapping
theorem, Michael’s selection theorem, Ekeland’s variational principle, and Kakutani’s
fixed point theorem
