No abstract

This paper is mainly devoted to present new sufficient conditions in terms of Fréchet coderivatives for the local metric regularity, the metric regularity, the Lipschitz-like property, the nonemptiness and the lower semicontinuity of random implicit multifunctions in separable Asplund spaces. An example is given to illustrate the above random implicit multifunction results. Some applications to stability analysis of solution maps for random parametric generalized equations are also given.

This paper is mainly devoted to the study of implicit multifunction theorems in terms of Clarke coderivative in general Banach spaces. We present new sufficient conditions for the local metric regularity, metric regularity, Lipschitz-like property, nonemptiness, and lower semicontinuity of implicit multifunctions in general Banach spaces. The basic tools of our analysis involve the Ekeland variational principle, the Clarke subdifferential, and the Clarke coderivative.