FRECHET AND PROXIMAL REGULARITIES OF PERTURBED DISTANCE FUNCTIONS AT POINTS IN THE TARGET SET IN BANACH SPACES

摘要

This paper is devoted to study the Frechet and proximal Regularity at points in the target set of perturbed distance functions d(S)(J)(.) determined by a closed subset S and a Lipschitz function J(.). Also, we provide some important results on the Clarke subdifferential of d(S)(J)(.) at those points in arbitrary Banach spaces.