Abstract
LET f: X → ℝ BE A function on a Banach space X. We say that f is strictly Gateaux differentiable if it is Gateaux differentiable at every point of X and the mapping (x, h) ↦ ’(x), h) is continuous. Recall that a convex Gateaux differentiable function is strictly Gateaux differentiable. In the case of a locally Lipschitz function our definition coincides with more standard ones: it requires that f’ be norm to weak-star continuous.
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