Abstract

This paper was motivated by the need to establish some new characterizations of the metric regularity of set-valued mappings. Through these new characterizations it was possible to investigate the global/local perturbation stability of the metric regularity and to extend a result by \textit{A. D. Ioffe} [Set-Valued Anal. 9, No. 1–2, 101–109 (2001; Zbl 1005.47045)] on the perturbation stability of the global metric regularity when the image space is not necessarily complete. It was also possible to give a characterization of the local metric regularity and to derive a local version of the perturbation stability of the metric regularity. In this work we also describe an application of this perturbation stability and give a simple proof of a result on the error bound of 2-regular mappings established by \textit{A. F. Izmailov} and \textit{M. V. Solodov} [Math. Program. 89, No. 3(A), 413–435 (2001; Zbl 1023.90062)] and generalized by \textit{Y. He} and \textit{J. Sun} [Math. Oper. Res. 30, No. 3, 701–717 (2005; Zbl 1082.90112)].