An Inverse Function Theorem for Metrically Regular Mappings
Optimization and Control
2007-05-23 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.math/0209222,
title = {An Inverse Function Theorem for Metrically Regular Mappings},
author = {Asen L. Dontchev},
journal= {arXiv preprint arXiv:math/0209222},
year = {2007}
}