Extensions of metric regularity†

Abstract

This article is devoted to some extensions of the metric regularity property for mappings between metric or Banach spaces. Several new concepts are investigated in a unified manner: uniform metric regularity, metric regularity along a subspace, metric multi-regularity for mappings into product spaces (when each component is perturbed independently), as well as their Lipschitz-like counterparts. The properties are characterized in terms of certain derivative-like constants. Regularity criteria are established based on a set-valued extension of a nonlocal version of the Lyusternik–Graves theorem due to Milyutin. †Dedicated to the memory of Prof. Dr. Alexender Moiseevich Rubinov; Guest Editors: Adil Bagirov and Gleb Beliakov.