Regularity of implicit solution mapping to parametric generalized equation

Abstract

This paper concerns the study of both local and global metric regularity/Lipschitz-like properties concerning the behavior of the implicit solution mapping associated to parametric generalized equation in metric space. We extend some implicit multifunction results to the addition of two multifunctions both depending on parameters. Through the approach of inverse mapping iteration, several results are established regarding the relations between the (partial) metric regularity/Lipschitz-like moduli of multifunctions used as the defining form of the generalized equation and the corresponding implicit solution mapping, the proof of which is completely self-contained. Finally, a local Lyusternik–Graves Theorem is obtained as an application.