Subdifferentials of a perturbed minimal time function in normed spaces

Abstract

In a general normed vector space, we study the perturbed minimal time function determined by a bounded closed convex set \(U\) and a proper lower semicontinuous function \(f(\cdot )\). In particular, we show that the Frechet subdifferential and proximal subdifferential of a perturbed minimal time function are representable by virtue of corresponding subdifferential of \(f(\cdot )\) and level sets of the support function of \(U\). Some known results is a special case of these results.