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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 S and a Lipschitz function J. Also, we provide some important results on the Fréchet, proximal, and Clarke subdifferentials of dSJ(⋅) at those points in Banach spaces.
We explore in arbitrary Banach spaces the Fréchet type ε-subdifferentials and the limiting subdifferentials for the perturbed distance function dSJ(⋅) determined by a closed subset S and a lower semicontinuous function J defined on S. In particular, upper and lower estimates for the Fréchet type ε-subdifferentials and for the limiting subdifferentials are provided in terms of the corresponding subdifferentials...
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