Subdifferential regularities of perturbed distance functions outside the target set in Banach spaces

This paper is devoted to study the Fréchet and proximal regularities at points outside the target set of perturbed distance functions dSJ(⋅) determined by a closed subset SS and a Lipschitz function JJ. Also, we provide some important results on the Fréchet, proximal, and Clarke subdifferentials of dSJ(⋅) at those points in Banach spaces.