Subdifferentials of a perturbed minimal time function in normed spaces

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

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