Stability of Implicit Multifunctions in Banach Spaces

This paper is devoted to present new sufficient conditions for both the metric regularity in the Robinson’s sense and the Lipschitz‐like property in the Aubin’s sense of implicit multifunctions in general Banach spaces. The basic tools of our analysis involve the Clarke subdifferential, the Clarke coderivative of set‐valued mappings, and the Ekeland variational principle. The metric regularity of implicit multifunction is compared with the Lipschitz‐like property.