An Inverse Function Theorem for Metrically Regular Mappings
Asen L. Dontchev
Abstract
We prove that if a mapping F:X to Y, where X and Y are Banach spaces, is metrically regular at x for y and its inverse F-1 is convex and closed valued locally around (x,y), then for any function G:X to Y with lip G(x)regF(x|y)) < 1, the mapping (F+G)-1 has a continuous local selection around (x, y+G(x)) which is also calm.
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