The paper is devoted to a revision of the metric regularity property for mappings between metric or Banach spaces. Some new concepts are introduced: uniform metric regularity, metric regularity along a subspace, strong metric regularity for mappings into product spaces, when each component is perturbed independently. Regularity criteria are established based on a nonlocal version of Lyusternik-Graves theorem due to Milyutin. The criteria are applied to systems of generalized equations producing some “error bound” type results
Citation
Published in J. Math. Anal. Appl. 342 (2008), no. 2, 864–873. The original publication is available at www.sciencedirect.com; doi:10.1016/j.jmaa.2007.12.057