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On robustness of the regularity property of maps

Ioffe A. D.

Control and Cybernetics

2003

Vol. 32, no 3

543-554

The problem considered in the paper can be described as follows. We are given a continuous mapping from one metric space into another which is regular (in the sense of metric regularity or, equivalently, controllability at a linear rate) near a certain point. How small may be an additive perturbation of the mapping which destroys regularity? The paper contains a new proof of a recent theorem of Dontchev-Lewis-Rockafellar for linear perturbations of maps between finite-dimensional Banach spaces and an exact estimate for Lipschitz perturbations of maps between complete metric spaces.