Preprint D18/2006
Directional regularity and metric regularity
A.F. Izmailov | Arutyunov, A.V. | Avakov, E.R.
Keywords: metric regularity | directional regularity
For general constraint systems in Banach spaces, we present the directional stability theorem based on the appropriate generalization of directional regularity condition, suggested earlier in [1]. This theorem contains Robinson's stability theorem but does not reduce to it. Furthermore, we develop the related concept of directional metric regularity which is stable subject to small Lipschitzian perturbations of the constraint mapping, and which is equivalent to directional regularity for sufficiently smooth mappings. Finally, we discuss some applications in sensitivity theory.