Differentiation of real-valued functions and continuity of metric projections
Differentiation of real-valued functions and continuity of metric projections
We characterize the Fréchet differentiability of real-valued functions on certain real Banach spaces in terms of a directional derivative being equal to a modified version of the local Lipschitz constant. This yields the continuity of metric projections onto closed sets whose distance functions have directional derivatives equal to 1, provided …