An inverse mapping theorem for set-valued maps

A. L. Dontchev, W. W. Hager
1994 Proceedings of the American Mathematical Society  
We prove that certain Lipschitz properties of the inverse F-1 of a set-valued map F are inherited by the map (f+F)~x when / has vanishing strict derivative.
doi:10.1090/s0002-9939-1994-1215027-7 fatcat:najjmry2mfemnelzwksqmqsemi